7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden · PDF filebewegung von körpern 16 7...

32
Bewegung von Körpern 16 7 (PSIHKOXQJHQ XQG 0DWHULD0 OLHQ ]XU 8QWHUULFKWVJHVWDOWXQJ 71 4 0HFKDQLN 1DFKGHP LQ .ODVVH ; HLQH HUVWH (LQIKUXQJ LQ GLH 6WRIIJHELHWH :lUPHOHKUH/ 2SWLN XQG (OHNWUL]LWlWV0 OHKUH HUIROJWH/ OLHJW LQ .ODVVH < HLQ 6FKZHUSXQNW DXI GHU %HKDQGOXQJ JUXQGOHJHQGHU %HJULIIH/ *HVHW]H XQG =XVDPPHQKlQJH GHU 0HFKDQLN1 ,QKDOWOLFKH 6FKZHUSXQNWH VLQG GDEHL ² GHU %HJULII *HVFKZLQGLJNHLW XQG VHLQH $QZHQGXQJ/ ² GLH &KDUDNWHULVLHUXQJ GHU SK\VLNDOLVFKHQ *U|H .UDIW XQG GLH %HKDQGOXQJ GHU :LUNXQJHQ YRQ .UlIWHQ/ ² GLH *HZLFKWVNUDIW ² GLH 0DVVH XQG GLH ’LFKWH DOV (LJHQVFKDIWHQ YRQ .|USHUQ E]Z 1 YRQ 6WRIIHQ/ ² GLH 5HLEXQJ XQG LKUH %HGHXWXQJ IU GLH 3UD[LV/ ² NUDIWXPIRUPHQGH (LQULFKWXQJHQ XQG GLH GDEHL ZLUNHQGHQ *HVHW]H/ ² GLH %HJULIIH PHFKDQLVFKH $UEHLW/ /HLVWXQJ XQG PHFKDQLVFKH (QHUJLH1 ’LH 1LYHDXV , XQG ,, XQWHUVFKHLGHQ VLFK LQKDOWOLFK LP 5DKPHQSODQ QXU XQZHVHQWOLFK1 ’HU 5DKPHQSODQ OlVVW DEHU HLQHQ EHPHUNHQVZHUW JURHQ ,QWHUSUHWDWLRQVVSLHO0 UDXP XQG HUP|JOLFKW GDGXUFK GLH $EGHFNXQJ XQWHU0 VFKLHGOLFKVWHU 1LYHDXV1 )U OHLVWXQJVVWlUNHUH 6FKOHU E]Z 1 .ODVVHQ EHVWHKW GDV K|KHUH 1LYHDX YRU DOOHP ² LQ GHU VWlUNHUHQ PDWKHPDWLVFKHQ ’XUFKGULQJXQJ GHV 6WRIIHV/ ² LQ GHU JU|HUHQ 6HOEVWVWlQGLJNHLW EHL GHU 9RUEHUHL0 WXQJ/ ’XUFKIKUXQJ XQG $XVZHUWXQJ YRQ ([SHUL0 PHQWHQ VRZLH EHL GHU /|VXQJ YRQ $XIJDEHQ/ ² LP K|KHUHQ 1LYHDX GHU $XIJDEHQ XQG ² LQ GHQ XPIDQJUHLFKHUHQ $QZHQGXQJHQ GHV :LVVHQV DXI 6DFKYHUKDOWH DXV 1DWXU / 7HFKQLN XQG $OOWDJ1 1DFKIROJHQG VLQG 9RUVFKOlJH XQWHUEUHLWHW/ GLH LQ EHL0 GHQ 1LYHDXV QXW]EDU VLQG1 71 41 4 %HZHJXQJ YRQ .|USHUQ %HL GHU %HKDQGOXQJ GHU %HZHJXQJ YRQ .|USHUQ VRO0 OHQ GLH 6FKOHU ² YHUVFKLHGHQH $UWHQ YRQ %HZHJXQJHQ NHQQHQ OHU0 QHQ XQG %HZHJXQJVDUWHQ YRQ .|USHUQ XQWHUVFKHL0 GHQ N|QQHQ> ² HUIDVVHQ/ GDVV %HZHJXQJ XQG 5XKH UHODWLY VLQG> ² GLH *HVFKZLQGLJNHLW HLQHV .|USHUV DOV 0D IU VHLQH 6FKQHOOLJNHLW HUNHQQHQ> ² GLH *OHLFKXQJ ]XU %HUHFKQXQJ GHU *HVFKZLQGLJ0 NHLW YV2W NHQQHQ XQG LQWHUSUHWLHUHQ N|QQHQ> ² *HVFKZLQGLJNHLWHQ EHUHFKQHQ XQG )ROJHUXQJHQ IU HLQ VLQQYROOHV 9HUKDOWHQ LP 6WUDHQYHUNHKU DEOHLWHQ N|QQHQ1 ,P 8QWHUULFKW VROOWH VHKU EHZXVVW DXI GLH YLHOIlOWLJHQ (UIDKUXQJHQ GHU 6FKOHU EHU %HZHJXQJHQ ]XUFN0 JHJULIIHQ ZHUGHQ XQG DXFK EHL 0HVVXQJHQ XQG $QZHQGXQJHQ LPPHU GHU %H]XJ ]XP (UIDKUXQJVEH0 UHLFK GHU 6FKOHU KHUJHVWHOOW ZHUGHQ1 $Q HLQIDFKHQ %HLVSLHOHQ +3HUVRQHQ DXI 5ROOWUHSSH/ )DKUJDVW LP =XJ RGHU DXI GHP 6FKLII,/ GLH DXFK LP .ODVVHQUDXP OHLFKW QDFKJHVWHOOW ZHUGHQ N|QQHQ/ ZLUG PLW GHQ 6FKOHUQ GLH )UDJH GLVNXWLHUW= :RUDQ HUNHQQW PDQ/ RE VLFK HLQ .|USHU LQ 5XKH RGHU LQ %HZHJXQJ EHILQGHW" ’LH 1RWZHQGLJNHLW GHU )HVWOHJXQJ HLQHV %H]XJVN|U0 SHUV ]XU HLQGHXWLJHQ .HQQ]HLFKQXQJ YRQ %HZHJXQJ XQG 5XKH ZLUG DQ GHQ REHQ JHQDQQWHQ %HLVSLHOHQ HU|UWHUW1 (V VROOWH DXFK YHUHLQEDUW ZHUGHQ/ GDVV PDQ ]XPHLVW GLH (UGREHUIOlFKH DOV %H]XJVN|USHU QLPPW XQG GLHV QLFKW H[WUD IRUPXOLHUW1 :LFKWLJ EHL GHU JHVDPWHQ %HWUDFKWXQJ LVW QXU= ’LH 6FKOHU VROOHQ HUIDVVHQ/ GDVV SK\VLNDOLVFKH $XVVDJHQ EHU 5XKH XQG %HZH0 JXQJ VHKU H[DNW IRUPXOLHUW ZHUGHQ PVVHQ/ ZHQQ VLH HLQGHXWLJ VHLQ VROOHQ1 %HL GHU %HKDQGOXQJ GHU $UWHQ YRQ %HZHJXQJHQ KDW HV VLFK EHZlKUW/ YRQ GHQ 6FKOHUQ %HLVSLHOH ]XVDPPHQ0 WUDJHQ ]X ODVVHQ/ GLHVH %HLVSLHOH DQ GHU 7DIHO LQ +IU GLH 6FKOHU ]XQlFKVW XQNODUH, *UXSSHQ ]X RUGQHQ XQG JHJHEHQHQIDOOV LQ HLQIDFKHQ ([SHULPHQWHQ DXI VSH]L0 HOOH $UWHQ YRQ %HZHJXQJHQ DXIPHUNVDP ]X PDFKHQ1 ’DV ZLUG YRU DOOHP EHL 6FKZLQJXQJHQ/ HYHQWXHOO DXFK EHL GHU .UHLVEHZHJXQJ GHU )DOO VHLQ1 1HEHQ GHU (LQEH]LHKXQJ GHU JHUDGOLQLJHQ %HZHJXQJ/ GHU .UHLVEHZHJXQJ XQG GHU 6FKZLQJXQJ NDQQ PDQ DXFK GLH ’UHKEHZHJXQJ PLW EHWUDFKWHQ/ GHQQ JHUDGH GDIU JLEW HV LP (UIDKUXQJVEHUHLFK GHU 6FKOHU ]DKO0 UHLFKH %HLVSLHOH1 ’LH 6XFKH GHU *HPHLQVDPNHLWHQ LQQHUKDOE GHU DQ GHU 7DIHO QRWLHUWHQ *UXSSHQ IKUW GDQQ ]X HLQHU (LQWHLOXQJ LQ $UWHQ YRQ %HZHJXQJHQ +V1 .RSLHUYRU0 ODJH,1 (LQH )HVWLJXQJ NDQQ DQKDQG HLQIDFKHU ([SHULPHQWH HUIROJHQ= ² (LQH .UHX]PXIIH PLW HLQJHVSDQQWHU %ODWWIHGHU +V1 $EE1, ZLUG VR DP 6WDWLY EHIHVWLJW/ GDVV VLH JHUDGH ]X UXWVFKHQ EHJLQQW/ ZHQQ GLH %ODWWIHGHU LQ 6FKZLQJXQJHQ YHUVHW]W ZLUG1 ’DV 6\VWHP .UHX]0 PXIIH ² %ODWWIHGHU VLQNW UXFNDUWLJ KHUDE/ GLH %ODWW0 IHGHU IKUW XQJHGlPSIWH 6FKZLQJXQJHQ DXV1 0LW +LOIH GHV DQ GHU %ODWWIHGHU EHIHVWLJWHQ 0DVVHVWFNV NDQQ GLH 6FKZLQJXQJVGDXHU YHUlQGHUW ZHUGHQ1

Transcript of 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden · PDF filebewegung von körpern 16 7...

Page 1: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

16

7 (PSIHKOXQJHQ#XQG#0DWHULD0OLHQ#]XU#8QWHUULFKWVJHVWDOWXQJ

71 4 0HFKDQLN

1DFKGHP# LQ#.ODVVH# ;# HLQH# HUVWH#(LQI�KUXQJ# LQ# GLH6WRIIJHELHWH# :lUPHOHKUH/# 2SWLN# XQG# (OHNWUL]LWlWV0OHKUH#HUIROJWH/#OLHJW#LQ#.ODVVH#<#HLQ#6FKZHUSXQNW#DXIGHU# %HKDQGOXQJ# JUXQGOHJHQGHU# %HJULIIH/# *HVHW]HXQG# =XVDPPHQKlQJH# GHU# 0HFKDQLN1# ,QKDOWOLFKH6FKZHUSXQNWH#VLQG#GDEHL² GHU#%HJULII#*HVFKZLQGLJNHLW#XQG#VHLQH#$QZHQGXQJ/² GLH# &KDUDNWHULVLHUXQJ# GHU# SK\VLNDOLVFKHQ# *U|�H.UDIW# XQG# GLH# %HKDQGOXQJ# GHU# :LUNXQJHQ# YRQ.UlIWHQ/

² GLH#*HZLFKWVNUDIW² GLH#0DVVH# XQG# GLH#'LFKWH# DOV#(LJHQVFKDIWHQ# YRQ.|USHUQ#E]Z1#YRQ#6WRIIHQ/

² GLH#5HLEXQJ#XQG#LKUH#%HGHXWXQJ#I�U#GLH#3UD[LV/² NUDIWXPIRUPHQGH# (LQULFKWXQJHQ# XQG# GLH# GDEHLZLUNHQGHQ#*HVHW]H/

² GLH# %HJULIIH# PHFKDQLVFKH# $UEHLW/# /HLVWXQJ# XQGPHFKDQLVFKH#(QHUJLH1

'LH#1LYHDXV#,#XQG#,,#XQWHUVFKHLGHQ#VLFK#LQKDOWOLFK# LP5DKPHQSODQ#QXU#XQZHVHQWOLFK1#'HU#5DKPHQSODQ#OlVVWDEHU#HLQHQ#EHPHUNHQVZHUW#JUR�HQ#,QWHUSUHWDWLRQVVSLHO0UDXP# XQG# HUP|JOLFKW# GDGXUFK# GLH#$EGHFNXQJ# XQWHU0VFKLHGOLFKVWHU#1LYHDXV1#)�U# OHLVWXQJVVWlUNHUH#6FK�OHUE]Z1#.ODVVHQ#EHVWHKW#GDV#K|KHUH#1LYHDX#YRU#DOOHP² LQ#GHU# VWlUNHUHQ#PDWKHPDWLVFKHQ#'XUFKGULQJXQJGHV#6WRIIHV/

² LQ#GHU#JU|�HUHQ#6HOEVWVWlQGLJNHLW#EHL#GHU#9RUEHUHL0WXQJ/#'XUFKI�KUXQJ#XQG#$XVZHUWXQJ#YRQ#([SHUL0PHQWHQ#VRZLH#EHL#GHU#/|VXQJ#YRQ#$XIJDEHQ/

² LP#K|KHUHQ#1LYHDX#GHU#$XIJDEHQ#XQG² LQ#GHQ#XPIDQJUHLFKHUHQ#$QZHQGXQJHQ#GHV#:LVVHQVDXI#6DFKYHUKDOWH#DXV#1DWXU/#7HFKQLN#XQG#$OOWDJ1

1DFKIROJHQG#VLQG#9RUVFKOlJH#XQWHUEUHLWHW/#GLH#LQ#EHL0GHQ#1LYHDXV#QXW]EDU#VLQG1

71 41 4 %HZHJXQJ#YRQ#.|USHUQ

%HL#GHU#%HKDQGOXQJ#GHU#%HZHJXQJ#YRQ#.|USHUQ#VRO0OHQ#GLH#6FK�OHU#

² YHUVFKLHGHQH#$UWHQ# YRQ#%HZHJXQJHQ#NHQQHQ# OHU0QHQ#XQG#%HZHJXQJVDUWHQ#YRQ#.|USHUQ#XQWHUVFKHL0GHQ#N|QQHQ>

² HUIDVVHQ/#GDVV#%HZHJXQJ#XQG#5XKH#UHODWLY#VLQG>² GLH# *HVFKZLQGLJNHLW# HLQHV# .|USHUV# DOV# 0D�# I�UVHLQH#6FKQHOOLJNHLW#HUNHQQHQ>

² GLH#*OHLFKXQJ# ]XU#%HUHFKQXQJ# GHU#*HVFKZLQGLJ0NHLW#Y# #V2W#NHQQHQ#XQG#LQWHUSUHWLHUHQ#N|QQHQ>

² *HVFKZLQGLJNHLWHQ# EHUHFKQHQ# XQG# )ROJHUXQJHQ

I�U# HLQ# VLQQYROOHV# 9HUKDOWHQ# LP# 6WUD�HQYHUNHKUDEOHLWHQ#N|QQHQ1

,P#8QWHUULFKW#VROOWH#VHKU#EHZXVVW#DXI#GLH#YLHOIlOWLJHQ(UIDKUXQJHQ#GHU#6FK�OHU#�EHU#%HZHJXQJHQ#]XU�FN0JHJULIIHQ# ZHUGHQ# XQG# DXFK# EHL# 0HVVXQJHQ# XQG$QZHQGXQJHQ#LPPHU#GHU#%H]XJ#]XP#(UIDKUXQJVEH0UHLFK#GHU#6FK�OHU#KHUJHVWHOOW#ZHUGHQ1

$Q# HLQIDFKHQ# %HLVSLHOHQ# +3HUVRQHQ# DXI# 5ROOWUHSSH/)DKUJDVW# LP#=XJ#RGHU#DXI#GHP#6FKLII,/#GLH#DXFK# LP.ODVVHQUDXP# OHLFKW# QDFKJHVWHOOW# ZHUGHQ# N|QQHQ/ZLUG#PLW#GHQ#6FK�OHUQ#GLH#)UDJH#GLVNXWLHUW=:RUDQ#HUNHQQW#PDQ/#RE#VLFK#HLQ#.|USHU#LQ#5XKH#RGHULQ#%HZHJXQJ#EHILQGHW"#'LH#1RWZHQGLJNHLW#GHU#)HVWOHJXQJ#HLQHV#%H]XJVN|U0SHUV#]XU#HLQGHXWLJHQ#.HQQ]HLFKQXQJ#YRQ#%HZHJXQJXQG#5XKH#ZLUG# DQ# GHQ# REHQ# JHQDQQWHQ#%HLVSLHOHQHU|UWHUW1(V#VROOWH#DXFK#YHUHLQEDUW#ZHUGHQ/#GDVV#PDQ#]XPHLVWGLH#(UGREHUIOlFKH#DOV#%H]XJVN|USHU#QLPPW#XQG#GLHVQLFKW# H[WUD# IRUPXOLHUW1# :LFKWLJ# EHL# GHU# JHVDPWHQ%HWUDFKWXQJ# LVW# QXU=# 'LH# 6FK�OHU# VROOHQ# HUIDVVHQ/GDVV# SK\VLNDOLVFKH#$XVVDJHQ#�EHU#5XKH#XQG#%HZH0JXQJ#VHKU#H[DNW#IRUPXOLHUW#ZHUGHQ#P�VVHQ/#ZHQQ#VLHHLQGHXWLJ#VHLQ#VROOHQ1

%HL#GHU#%HKDQGOXQJ#GHU#$UWHQ#YRQ#%HZHJXQJHQ#KDW#HVVLFK#EHZlKUW/#YRQ#GHQ#6FK�OHUQ#%HLVSLHOH#]XVDPPHQ0WUDJHQ#]X#ODVVHQ/#GLHVH#%HLVSLHOH#DQ#GHU#7DIHO#LQ#+I�U#GLH6FK�OHU# ]XQlFKVW# XQNODUH,# *UXSSHQ# ]X# RUGQHQ# XQGJHJHEHQHQIDOOV# LQ# HLQIDFKHQ#([SHULPHQWHQ# DXI# VSH]L0HOOH#$UWHQ#YRQ#%HZHJXQJHQ#DXIPHUNVDP#]X#PDFKHQ1'DV#ZLUG#YRU#DOOHP#EHL#6FKZLQJXQJHQ/#HYHQWXHOO#DXFKEHL#GHU#.UHLVEHZHJXQJ#GHU#)DOO#VHLQ1

1HEHQ#GHU#(LQEH]LHKXQJ#GHU#JHUDGOLQLJHQ#%HZHJXQJ/GHU#.UHLVEHZHJXQJ#XQG#GHU#6FKZLQJXQJ#NDQQ#PDQDXFK#GLH#'UHKEHZHJXQJ#PLW#EHWUDFKWHQ/#GHQQ#JHUDGHGDI�U#JLEW#HV#LP#(UIDKUXQJVEHUHLFK#GHU#6FK�OHU#]DKO0UHLFKH#%HLVSLHOH1

'LH# 6XFKH# GHU#*HPHLQVDPNHLWHQ# LQQHUKDOE# GHU# DQGHU# 7DIHO# QRWLHUWHQ# *UXSSHQ# I�KUW# GDQQ# ]X# HLQHU(LQWHLOXQJ# LQ#$UWHQ#YRQ#%HZHJXQJHQ# +V1#.RSLHUYRU0ODJH,1

(LQH#)HVWLJXQJ#NDQQ#DQKDQG#HLQIDFKHU#([SHULPHQWHHUIROJHQ=² (LQH#.UHX]PXIIH#PLW#HLQJHVSDQQWHU#%ODWWIHGHU#+V1$EE1,#ZLUG#VR#DP#6WDWLY#EHIHVWLJW/#GDVV#VLH#JHUDGH]X# UXWVFKHQ# EHJLQQW/# ZHQQ# GLH# %ODWWIHGHU# LQ6FKZLQJXQJHQ# YHUVHW]W#ZLUG1#'DV#6\VWHP#.UHX]0PXIIH#²#%ODWWIHGHU#VLQNW#UXFNDUWLJ#KHUDE/#GLH#%ODWW0IHGHU# I�KUW# XQJHGlPSIWH# 6FKZLQJXQJHQ# DXV1#0LW+LOIH#GHV#DQ#GHU#%ODWWIHGHU#EHIHVWLJWHQ#0DVVHVW�FNVNDQQ#GLH#6FKZLQJXQJVGDXHU#YHUlQGHUW#ZHUGHQ1

Page 2: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

17

² (LQH# HQWVSUHFKHQGH# $QRUGQXQJ# JLEW# HV# DXFK# DOV6SLHO]HXJ1# 'LH# %ODWWIHGHU# LVW# GRUW# HUVHW]W# GXUFKHLQHQ#6SHFKW#+SLFNHQGHU#6SHFKW,1#,Q#EHLGHQ#)lOOHQLVW#HLQH#6FKZLQJXQJ#+)HGHU,#XQG#HLQH#+IDVW,#JHUDG0OLQLJH#%HZHJXQJ#+.UHX]PXIIH,#]X#EHREDFKWHQ1

² 'DV#5DG#HLQHV#)DKUUDGHV#ZLUG#JHGUHKW1#'DEHL#NDQQVHKU# VFK|Q# GHU# 8QWHUVFKLHG# ]ZLVFKHQ# .UHLVEHZH0JXQJ# +HLQHV#3XQNWHV#GHV#.|USHUV,#XQG#'UHKEHZH0JXQJ#+GHV#.|USHUV#XP#HLQH#$FKVH,#HU|UWHUW#ZHUGHQ1

² (LQ#6SLHO]HXJDXWR# IlKUW#DXI#GHP#7LVFK1#(V#WUHWHQJHUDGOLQLJH#%HZHJXQJ#XQG#'UHKEHZHJXQJ#+5lGHU,DXI1#$XI#GLH# UHODWLY#NRPSOL]LHUWH#%HZHJXQJ# HLQHV3XQNWHV#DP#5DG#NDQQ#LQ#OHLVWXQJVVWDUNHQ#.ODVVHQHLQJHJDQJHQ#ZHUGHQ1

:HLWHUH# $XIJDEHQ# ]XU# )HVWLJXQJ# VLQG# LP# /%# 61# 47XQG#LP#$+#61#4#HQWKDOWHQ1

'HU#%HJULII#*HVFKZLQGLJNHLW# LVW#ZRKO#DOOHQ#6FK�0OHUQ# EHNDQQW1# 'LH# PHLVWHQ# YRQ# LKQHQ# YHUELQGHQGDPLW#GXUFKDXV#ULFKWLJH/#ZHQQ#DXFK#]XPHLVW#XQYROO0VWlQGLJH# 9RUVWHOOXQJHQ1# 6R# ZLUG# *HVFKZLQGLJNHLWKlXILJ# QXU# PLW# VFKQHOOHQ# %HZHJXQJHQ# YHUNQ�SIW/ODQJVDPHQ#%HZHJXQJHQ#ZLUG#NHLQH#*HVFKZLQGLJNHLW]XJHRUGQHW1#9RQ# GLHVHQ#$OOWDJVYRUVWHOOXQJHQ# DXVJH0KHQG/# VROOWHQ# EHL# GHU# XQWHUULFKWOLFKHQ# %HKDQGOXQJHLQLJH# 6FKZHUSXQNWH# JHVHW]W# ZHUGHQ1# ,KUH# 5HLKHQ0IROJH#LVW#]XJOHLFK#HLQ#EHZlKUWHU#:HJ#GHU#(LQI�KUXQJXQG#)HVWLJXQJ#GHV#*HVFKZLQGLJNHLWVEHJULIIHV1² $Q# %HLVSLHOHQ# DXV# LKUHP# (UIDKUXQJVEHUHLFK# XQGEHL# HLQIDFKHQ# ([SHULPHQWHQ# +6SLHO]HXJDXWR/0RGHOOHLVHQEDKQ/# ODQJVDPHV#XQG#VFKQHOOHV#5ROOHQHLQHV# %DOOHV,# ZLUG# KHUDXVJHDUEHLWHW/# GDVV# %HZH0JXQJHQ#YRQ#.|USHUQ#ODQJVDP#RGHU#VFKQHOO#YHUODX0IHQ1

² =XU# JHQDXHUHQ# &KDUDNWHULVLHUXQJ# GHU# 6FKQHOOLJ0NHLW#GHU#%HZHJXQJ#HLQHV#.|USHUV#JLEW#HV#GUHL#0|J0OLFKNHLWHQ#+V1#/%#61#;,1D,0DQ#N|QQWH#DQJHEHQ/#ZHOFKHQ#:HJ#HLQ#.|USHULQ#HLQHU#EHVWLPPWHQ#=HLW# +]1 %1# LQ#4#V#RGHU#4#K,]XU�FNOHJW1#'HU#.|USHU/#GHU#GHQ#JU|�HUHQ#:HJ]XU�FNOHJW/# LVW# VFKQHOOHU1# +%HLVSLHO=# :HJ# HLQHV$XWRV#XQG#HLQHV#)DKUUDGIDKUHUV#LQ#4#K,1

E,0DQ# N|QQWH# DQJHEHQ/# ZHOFKH# =HLW# HLQ# .|USHUI�U#HLQHQ#EHVWLPPWHQ#:HJ#EUDXFKW1#'HU#.|USHU/

GHU# GLH#N�U]HUH#=HLW#EUDFKW/# LVW# VFKQHOOHU# +%HL0VSLHO=#4330P0/DXI,1

F,0DQ# N|QQWH# GLH# *HVFKZLQGLJNHLW# GHV# .|USHUVDQJHEHQ1#6LH#LVW#GHILQLHUW#DOV#Y# #V2W1

² %HL# HLQHU# JOHLFKI|UPLJHQ# %HZHJXQJ# LVW# GLH*HVFKZLQGLJNHLW# NRQVWDQW/# EHL# HLQHU# XQJOHLFKI|U0PLJHQ#%HZHJXQJ#HUKlOW#PDQ#DXV#GHP#]XU�FNJHOHJ0WHQ# :HJ# XQG# GHU# EHQ|WLJWHQ# =HLW# GLH# 'XUFK0VFKQLWWVJHVFKZLQGLJNHLW1

,P#ZHLWHUHQ#VROOWH#HLQH#.RQ]HQWUDWLRQ#DXI#JOHLFKI|U0PLJH#%HZHJXQJHQ#HUIROJHQ#XQG#GDEHL#GLH#*OHLFKXQJY# #V2W#VRZLH#VSH]LHOOH#*HVFKZLQGLJNHLWHQ#+V1#7DEHOOHLP#/%#61#;,#LQWHUSUHWLHUW#ZHUGHQ/#]1#%1#GXUFK#)UDJHQZLH=² :DV#EHGHXWHW=#Å(LQ#$XWR#EHZHJW#VLFK#PLW#83 NP2K´"#² :HOFKHQ# :HJ# OHJW# HLQ# )X�JlQJHU/# GHU# VLFK# PLW4/5 P2V#EHZHJW/#LQ#4#V/#5#V/#43#V#]XU�FN"

² ,Q# ZHOFKHU# =HLW# OHJW# HLQ# 5DGIDKUHU/# GHU# VLFK#PLWHLQHU#*HVFKZLQGLJNHLW#YRQ#48#NP2K#EHZHJW/#8#NP/48#NP/#63#NP#]XU�FN"

² +DW# DXFK# HLQH# NULHFKHQGH# 6FKQHFNH# HLQH# *H0VFKZLQGLJNHLW"

$QKDQG# HLQHU# VSH]LHOOHQ# JOHLFKI|UPLJHQ# %HZHJXQJN|QQHQ# LP# '(# +:HJ0=HLW00HVVXQJHQ,# PLW# DQVFKOLH0�HQGHU# JHPHLQVDPHU# $XVZHUWXQJ# XQWHUVFKLHGOLFKH0|JOLFKNHLWHQ#GHU#&KDUDNWHULVLHUXQJ#HLQHU#JOHLFKI|U0PLJHQ# %HZHJXQJ# YHUGHXWOLFKW# ZHUGHQ1# 8P# GDV*HPHLQVDPH#XQG#GDV#8QWHUVFKLHGOLFKH#GDEHL#GHXWOLFKZHUGHQ# ]X# ODVVHQ/# VLQG#PLQGHVWHQV# ]ZHL#0HVVUHLKHQEHL#XQWHUVFKLHGOLFKHQ#*HVFKZLQGLJNHLWHQ#HUIRUGHUOLFK1(V#HUJHEHQ#VLFK#LQ#$XVZHUWXQJ#GHU#0HVVUHLKHQ#GLH#LP7%#+V1#QlFKVWH#6HLWH,#GDUJHVWHOOWHQ#0|JOLFKNHLWHQ#GHU&KDUDNWHULVLHUXQJ#JOHLFKI|UPLJHU#%HZHJXQJHQ1

%HL#GHU#)HVWLJXQJ#ELHWHQ# VLFK#YHUVFKLHGHQH#6FKZHU0SXQNWH#DQ/#GLH#LQ#$EKlQJLJNHLW#YRQ#GHU#.ODVVHQVLWXD0WLRQ# XQG# GHU# 8QWHUULFKWVNRQ]HSWLRQ# GHV# /HKUHUVXQWHUVFKLHGOLFK#JHZLFKWHW#ZHUGHQ#N|QQHQ=

41'LH# 6FK�OHU# VROOWHQ# DXI# MHGHQ# )DOO#:HJ0=HLW00HV0VXQJHQ# VHOEVW# GXUFKI�KUHQ# XQG# GLH# 0HVVZHUWHUHFKQHULVFK# XQG# JUDILVFK# +V0W0'LDJUDPP,# DXVZHU0WHQ1#(LQH#DXVI�KUOLFKH#([SHULPHQWLHUDQOHLWXQJ#LVWLP#$+#+61#5 ²6,#HQWKDOWHQ1

51 ,QWHUHVVDQWH#0|JOLFKNHLWHQ#GHU#8QWHUULFKWVJHVWDO0WXQJ#ELV#KLQ#]X#SURMHNWDUWLJHQ#$UEHLWHQ#ELHWHW#GLH)UDJH# GHU# *HVFKZLQGLJNHLWVPHVVXQJ1# 0LW# GHQ6FK�OHUQ# N|QQWH# HU|UWHUW# ZHUGHQ/#ZLH#PDQ# ]1 %1GLH#*HVFKZLQGLJNHLW# HLQHV#5DGIDKUHUV/# HLQHV#%DO0OHV/#HLQHV#$XWRV/#HLQHV#/lXIHUV#PLW#HLQIDFKHQ#0LW0WHOQ#EHVWLPPHQ#NDQQ1#(U|UWHUWH#0|JOLFKNHLWHQ#GHU*HVFKZLQGLJNHLWVEHVWLPPXQJ# VROOWHQ/# ZHQQ# GDVEHL# GHQ# JHJHEHQHQ# %HGLQJXQJHQ# UHDOLVLHUEDU# LVW/DXFK#DXVSURELHUW#ZHUGHQ1

Page 3: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

18

#.RSLHUYRUODJH

%HZHJXQJ#YRQ#.|USHUQ

(LQ#.|USHU#LVW

LQ#%HZHJXQJ LQ#5XKH

lQGHUW QLFKW#lQGHUW

:LU#XQWHUVFKHLGHQ#IROJHQGH#$UWHQ#YRQ#%HZHJXQJHQ=

(LQH#%HZHJXQJ#NDQQ#HUIROJHQ

:(11#(5#6(,1(#/$*(#*(*(1h%(5#(,1(0#%(=8*6.g53(5

*HUDGOLQLJH%HZHJXQJ

.UHLVEHZHJXQJ 'UHKEHZHJXQJ 6FKZLQJXQJ

$XWR#DXI#JHUDGHU#6WUHFNH

*RQGHO#HLQHV5LHVHQUDGHV

%RKUHU#HLQHU#%RKUPDVFKLQH

3HQGHO#HLQHU#8KU

JOHLFKI|UPLJ XQJOHLFKI|UPLJ

'LH#*HVFKZLQGLJNHLW#EOHLEW#LPPHU#JOHLFK#JUR�1

EHVFKOHXQLJW YHU]|JHUW

'LH#*HVFKZLQGLJNHLW#QLPPW#]X1

'LH#*HVFKZLQGLJNHLW#QLPPW#DE1

]1 %1#PLW#NRQVWDQWHU#*HVFKZLQGLJNHLW#IDK0UHQGHV#$XWR

]1 %1#DQIDKUHQGHU#=XJ

]1 %1EUHPVHQGHU#5DGIDKUHU

Page 4: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

19

7DIHOELOG

7DIHOELOG#

'LH#*HVFKZLQGLJNHLW#YRQ#.|USHUQ

'LH#*HVFKZLQGLJNHLW#JLEW#DQ/#ZLH#VFKQHOO#RGHU#ODQJVDP#VLFK#HLQ#.|USHU#EHZHJW1

%HL#GHU#JOHLFKI|UPLJHQ#%HZHJXQJ#LVW#GLH#*HVFKZLQGLJNHLW#LPPHU#JOHLFK#JUR�1

%HL#GHU#XQJOHLFKI|UPLJHQ#%HZHJXQJ#lQGHUW#VLFK#GLH#*HVFKZLQGLJNHLW1$XV#GHP#]XU�FNJHOHJWHQ#:HJ#XQG#GHU#EHQ|WLJWHQ#=HLW#HUKlOW#PDQ#GLH#'XUFKVFKQLWWV0JHVFKZLQGLJNHLW1

*HVFKZLQGLJNHLW ]XU�FNJHOHJWHU#:HJ

EHQ|WLJWH#=HLW000000000000000000000000000000000000000000000000000000

Y VW00

(LQKHLWHQ#GHU#*HVFKZLQGLJNHLW

4kNP

K000000000 1m

6 9 V/000000000000 4kP

V00000. 6 9 kNP

K000000000/

'LH#JOHLFKI|UPLJH#%HZHJXQJ

0HVVXQJ#4 0HVVXQJ#5

(LQH#JOHLFKI|UPLJH#%HZHJXQJ#OLHJW#YRU/#ZHQQ�#Y# #V2W#NRQVWDQW#LVW/

�#GHU#.|USHU#LQ#JOHLFKHQ#=HLWHQ#JOHL0FKH#:HJH#]XU�FNOHJW/

�#GLH#0HVVZHUWHSDDUH#LP#V0W0'LD0JUDPP#DXI#HLQHU#*HUDGHQ#OLHJHQ/#GLH#GXUFK#GHQ#1XOOSXQNW#YHUOlXIW1

W#LQ#V

WLQ#V

VLQ#FP

V#LQ#FP

Y# #V2W#LQ#FP2V

Y# #V2W#LQ#FP2V

Page 5: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

20

61(LQ# (UNXQGXQJVDXIWUDJ# I�U# GLH# 6FK�OHU# N|QQWHGDULQ#EHVWHKHQ/# LQ#(UJlQ]XQJ# ]X#GHU# LP#/%#61# ;HQWKDOWHQHQ# hEHUVLFKW# *HVFKZLQGLJNHLWHQ# YRQ.|USHUQ#LQ#1DWXU#XQG#7HFKQLN#KHUDXV]XILQGHQ1#,QGLHVHP# =XVDPPHQKDQJ# N|QQHQ# GLH# 6FK�OHU# DXIVSH]LHOOH#(LQKHLWHQ#GHU#*HVFKZLQGLJNHLW#+EHL#6FKLI0IHQ=#4#.QRWHQ# 4#6HHPHLOH26WG1# 4#;85#NP2K>#EHL)OXJ]HXJHQ=#4#0DFK# #673#P2V# #4#533#NP2K,#DXI0PHUNVDP#JHPDFKW#ZHUGHQ1(LQHQ#hEHUEOLFN#�EHU#*HVFKZLQGLJNHLWHQ#LQ#1DWXUXQG#7HFKQLN#JLEW#GLH#EHLOLHJHQGH#.RSLHUYRUODJH1

71%HL# GHU# $UEHLW# PLW# V0W0'LDJUDPPHQ# VROOWHQ# LP8QWHUULFKW#IROJHQGH#$VSHNWH#HLQH#5ROOH#VSLHOHQ=� =HLFKQHQ# YRQ# V0W0'LDJUDPPHQ/# P|JOLFKVW# LP=XVDPPHQKDQJ# PLW# ([SHULPHQWHQ/# GDPLW# GLH6FK�OHU# HLQH#%H]LHKXQJ# ]ZLVFKHQ# HLQHP# UHDOHQ6DFKYHUKDOW#XQG#GHU#DEVWUDNWHQ#JUDILVFKHQ#'DU0VWHOOXQJ#KHUVWHOOHQ#N|QQHQ1'DEHL#VROOWH#YRQ#YRUQKHUHLQ#DXI#GDV#3UREOHP#YRQ0HVVIHKOHUQ# XQG# DXI# GLH# GDUDXV# UHVXOWLHUHQGH%HUHFKWLJXQJ#GHV#=HLFKQHQV#HLQHU#$XVJOHLFKVJH0UDGHQ#DXIPHUNVDP#JHPDFKW#ZHUGHQ1#'D]X#NDQQGDV#$+#61#4#JHQXW]W#ZHUGHQ1

7DIHOELOG

UDGHQ#DXIPHUNVDP#JHPDFKW#ZHUGHQ1#'D]X#NDQQGDV#$+#61#4#JHQXW]W#ZHUGHQ1� ,QWHUSUHWLHUHQ#YRQ#V0W0'LDJUDPPHQ=#$EOHVHQ#YRQ:HJHQ#EHL#XQWHUVFKLHGOLFKHQ#=HLWHQ/#$EOHVHQ#YRQ=HLWHQ#EHL#XQWHUVFKLHGOLFKHQ#:HJHQ/#(U|UWHUQ#GHU%HGHXWXQJ#GHU#6WHLOKHLW#GHU#.XUYH#+V1#7%,1

81$QZHQGXQJVDXIJDEHQ# VROOWHQ# EHZXVVW# VR# DXVJH0ZlKOW#ZHUGHQ/#GDVV#VLH#GHQ#(UIDKUXQJVEHUHLFK#GHU6FK�OHU# WDQJLHUHQ# XQG# LKQHQ# DXFK# SUDNWLVFKH/HEHQVKLOIH#JHEHQ1#'D]X#JHK|UHQ#]1#%1� $XIJDEHQ#LP#=XVDPPHQKDQJ#PLW#GHU#Å6FKUHFN0VHNXQGH´# LP#6WUD�HQYHUNHKU# HLQVFKOLH�OLFK# GHU$EOHLWXQJ#YRQ#)ROJHUXQJHQ#I�U#GDV#HLJHQH#+DQ0GHOQ#+V1#/%#61#44 ² 45,>

� $XIJDEHQ# LP# =XVDPPHQKDQJ# PLW# )DKUSOlQHQ+/%#61#48,/

� $XIJDEHQ/#GLH#9RUVWHOOXQJHQ#GDU�EHU#YHUPLWWHOQ/ZLH#VFKQHOO#PDQ#VLFK#VHOEVW#XQG#ZLH#VFKQHOO#VLFKDQGHUH# 3HUVRQHQ# XQG# .|USHU# EHZHJHQ1# $XFKGD]X#VLQG#LP#/%#+61#47 ² 48,#HLQLJH#$XIJDEHQ#HQW0KDOWHQ1

'DV#:HJ0=HLW0'LDJUDPP

0HVVZHUWH

W#LQ#V 5 7 9

V#LQ#FP 48 5; 6<

W#LQ#V ; 43 45

V#LQ#FP 88 9: :;

$XV#GHP#V0W0'LDJUDPP#LVW#DEOHVEDU=

²GHU#:HJ/#GHU#QDFK#HLQHU#EHVWLPPWHQ#=HLW#]XU�FNJHOHJW#ZXUGH#+]1#%1=#1DFK#45#V#VLQG#;3 FP#]XU�FNJHOHJW1,/²GLH#=HLW/#GLH#I�U#HLQHQ#EHVWLPPWHQ#:HJ#EHQ|WLJW#ZXUGH#+]1#%1=#)�U#73#FP#ZHUGHQ#HWZD#9#V#EHQ|WLJW1,/²GLH#*HVFKZLQGLJNHLW=#-H#VWHLOHU#GLH#.XUYH#LVW/#GHVWR#JU|�HU#LVW#GLH#*HVFKZLQGLJNHLW#GHV#.|USHUV1

Page 6: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Bewegung von Körpern

21

#.RSLHUYRUODJH

*HVFKZLQGLJNHLWHQ#LQ#1DWXU#XQG#7HFKQLN

Page 7: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

22

71 41 5 .UlIWH#XQG#LKUH#:LUNXQJHQ

'HU#%HJULII#GHU#.UDIW#LVW#HLQHU#GHU#]HQWUDOHQ#%HJULIIHLP#3K\VLNXQWHUULFKW1#(V#LVW#]XJOHLFK#HLQ#%HJULII/#GHV0VHQ#VDXEHUH#(LQI�KUXQJ#XQG#GHVVHQ#$EJUHQ]XQJ#]XDQGHUHQ#%HJULIIHQ/#HWZD#]XU#0DVVH#RGHU#]XP#'UXFN/HUIDKUXQJVJHPl�#LPPHU#ZLHGHU#3UREOHPH#EHUHLWHW1)�U#GLH#XQWHUULFKWOLFKH#$EIROJH#HUVFKHLQW#GHVKDOE#LP8QWHUVFKLHG# ]XP# 5DKPHQSODQ# IROJHQGH# 9DULDQWH]ZHFNPl�LJ=² (V#ZLUG#GHU#%HJULII#.UDIW#DXI#EUHLWHU#HPSLULVFKHU*UXQGODJH#HLQJHI�KUW1

² $OV#VSH]LHOOH#.UDIW#ZLUG#GLH#*HZLFKWVNUDIW#EHKDQGHOW1² $OV#ZHLWHUH#VSH]LHOOH#.UDIW#ZLUG#GLH#5HLEXQJVNUDIWEHWUDFKWHW1

² $QVFKOLH�HQG#ZHUGHQ#.|USHU0#XQG#6WRIIHLJHQVFKDI0WHQ#+0DVVH/#'LFKWH,#LQ#GHQ#9RUGHUJUXQG#JHVWHOOW1

² %HL#GHQ#NUDIWXPIRUPHQGHQ#(LQULFKWXQJHQ#ZHUGHQGLH#YRUKHU#HUZRUEHQHQ#.HQQWQLVVH#DQJHZHQGHW1

'LH# ZHVHQWOLFKHQ# 8QWHUVFKLHGH# ]ZLVFKHQ# 1LYHDX# ,XQG#1LYHDX#,,#EHVWHKHQ#GDULQ/#GDVV#EHLP#1LYHDX#,,² .UlIWH#DOV#9HNWRUHQ#GDUJHVWHOOW#ZHUGHQ/² GLH#=XVDPPHQVHW]XQJ#XQG#=HUOHJXQJ#YRQ#.UlIWHQVRZLH#GDV#.UlIWHJOHLFKJHZLFKW#EHKDQGHOW#ZHUGHQ/

² QHEHQ#GHQ#$UWHQ#YRQ#5HLEXQJ#DXFK#5HLEXQJVNUlIWHLQ#GLH#%HWUDFKWXQJHQ#HLQEH]RJHQ#ZHUGHQ1

'HU#%HJULII#.UDIW#LVW#GHQ#6FK�OHUQ#DXV#GHU#8PJDQJV0VSUDFKH#EHNDQQW/#HEHQVR#DXFK#:LUNXQJHQ#YRQ#.UlI0WHQ1# ,P# 3K\VLNXQWHUULFKW# VROOWH# DQ# GLHVH# 9RU0HUIDKUXQJHQ#GHU#6FK�OHU#DQJHNQ�SIW#ZHUGHQ/#ZREHLHV# ]XQlFKVW#XP# HLQH#3Ul]LVLHUXQJ#GHU#%HJULIIH#XQGXP#HLQH#6\VWHPDWLVLHUXQJ#YRQ#9RUNHQQWQLVVHQ#JHKW1(LQ# HUVWHU# 6FKZHUSXQNW# LVW# GLH# &KDUDNWHULVLHUXQJGHU# .UDIW# DOV# :HFKVHOZLUNXQJVJU|�H# XQG# DOV# HLQH*U|�H/# GLH# 9HUIRUPXQJHQ# +=HUVW|UXQJ,# RGHU# %HZH0JXQJVlQGHUXQJHQ#KHUYRUUXIHQ#NDQQ18P#GLHVH#0HUNPDOH#KHUDXV]XDUEHLWHQ/#LVW#HV#]ZHFN0Pl�LJ/# QHEHQ# GHQ# %H]�JHQ# ]X# $OOWDJVHUIDKUXQJHQGHU#6FK�OHU#DXFK#HLQLJH#([SHULPHQWH#GXUFK]XI�KUHQ1'DEHL# VROOWHQ# MHZHLOV# GLH# LQWHUHVVLHUHQGHQ# $VSHNWHKHUYRUJHKREHQ#ZHUGHQ=²# (V#ZLUNHQ# LPPHU# +PLQGHVWHQV,# ]ZHL#.|USHU# DXI0HLQDQGHU#HLQ1

²# 'DEHL# WUHWHQ# 9HUIRUPXQJHQ# +=HUVW|UXQJHQ,# RGHUbQGHUXQJHQ#GHU#%HZHJXQJ#DXI1

*HHLJQHW#VLQG#EHLVSLHOVZHLVH#IROJHQGH#([SHULPHQWH=²# (LQ# JUR�HV#:lJHVW�FN# +]1 %1# 4# NJ,#ZLUG# JHKREHQRGHU#DXI#GHP#7LVFK#YHUVFKREHQ1

²# (LQH# )HGHU# +HLQ# ([SDQGHU,# ZLUG# PLW# GHU# +DQGJHGHKQW#E]Z1#ZLUG#YRQ#]ZHL#6FK�OHUQ#DXVHLQDQGHU0JH]RJHQ1

²# =ZHL#NOHLQH#([SHULPHQWLHUZDJHQ#ZHUGHQ#PLW#GHP)HGHUVWR�JHUlW#QDFK#OLQNV#E]Z1#QDFK#UHFKWV#EHZHJW+V1 6NL]]H,1

²# .QHWH#ZLUG#YHUIRUPW1²# (LQ#7RQQHQIX�# IlOOW#DXI#HLQH#)HGHU#XQG#YHUIRUPWVLH#+V1#6NL]]H,1

² (LQ# 6W�FN# :�UIHO]XFNHU# ZLUG# PLW# +LOIH# HLQHU=DQJH#]HUNOHLQHUW#+]HUVW|UW,1

9HUZLHVHQ#ZHUGHQ# NDQQ# DXFK# DXI# GLH# LP# /%# 61# 4;JHQDQQWHQ#%HLVSLHOH1'LH# $EKlQJLJNHLW# GHU# :LUNXQJHQ# HLQHU# .UDIW# YRQ%HWUDJ/# 5LFKWXQJ# XQG# $QJULIIVSXQNW# N|QQHQ# PLWHLQHU#([SHULPHQWLHUIROJH#HQWVSUHFKHQG#GHU#'DUVWHO0OXQJ#LP#/%#61#5:#GHPRQVWULHUW#ZHUGHQ1#0DQ#EHQ|WLJWGD]X#OHGLJOLFK#HLQH#+RO]OHLVWH#RGHU#HLQH#%ODWWIHGHU/#DQGHU# PHKUHUH# 6FKODXIHQ# EHIHVWLJW# VLQG/# XQG# HLQHQ)HGHUNUDIWPHVVHU1#$QDORJ#OlVVW#VLFK#DXFK#HLQ#([SHULPHQW#]XU#bQGHUXQJGHU#%HZHJXQJ#YRQ#.|USHUQ#EHLP#XQWHUVFKLHGOLFKHQ(LQZLUNHQ#HLQHU#.UDIW#DXI#HLQHQ#.|USHU#GXUFKI�KUHQ+V1#6NL]]H,1

=XU#)HVWLJXQJ#ELHWHQ#GDV#$+#61#7#XQG#GDV#/%#61 68#II1HLQ#$XIJDEHQDQJHERW1'LH#7DEHOOH#LP#/%#61#53#YHUPLWWHOW#HLQLJH#*U|�HQYRU0VWHOOXQJHQ#�EHU#.UlIWH1#'LH#6FK�OHU#VROOWHQ#DQJHUHJWZHUGHQ#]X#HUNXQGHQ/#ZHOFKH#%HWUlJH#.UlIWH#LQ#1DWXUXQG#7HFKQLN#DQQHKPHQ#N|QQHQ1#'D]X#JHK|UHQ# LQV0EHVRQGHUH# DXFK# .|USHUNUlIWH/# GLH# ]1 %1# PLW# +LOIHHLQHV#([SDQGHUV#YHUJOLFKHQ#ZHUGHQ#N|QQHQ1'DPLW# HUIROJW# ]XJOHLFK# HLQH# 9RUEHUHLWXQJ# DXI# GLH.UDIWPHVVXQJ1#(V# LVW# I�U# GLH# 6FK�OHU#PHLVW# VFKQHOOHLQVHKEDU/# GDVV# GLH# 9HUIRUPXQJ# HLQHV# .|USHUV# JXWJHHLJQHW# LVW/#XP#.UlIWH#PLWHLQDQGHU# ]X# YHUJOHLFKHQXQG# ]X#PHVVHQ1#'LH#(LQEH]LHKXQJ# HLQHV#([SDQGHUVRGHU#HLQHU#)HGHU#PLW#JUR�HU#)HGHUNRQVWDQWHQ#LQ#GHQ8QWHUULFKW# LVW# HPSIHKOHQVZHUW1# (V# NDQQ# DXFK# HLQNOHLQHU# :HWWEHZHUE# JHVWDOWHW# ZHUGHQ=# (V# OHXFKWHWMHGHP#6FK�OHU#HLQ/#GDVV#GHUMHQLJH#HLQH#JU|�HUH#.UDIW

Page 8: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

23

DXV�EW/#GHU#GHQ#([SDQGHU#+GLH#)HGHU,#PHKU#GHKQW1$EOHVH�EXQJHQ# DQ#)HGHUNUDIWPHVVHUQ# VROOWH# KLQUHL0FKHQG#$XIPHUNVDPNHLW# JHZLGPHW#ZHUGHQ1#%HZlKUWKDW# VLFK#GDI�U#GLH#1XW]XQJ# HLQHU#)ROLH/#DXI#GHU#GLH6NDOHQ#GHU#)HGHUNUDIWPHVVHU#DXIJH]HLFKQHW#VLQG/#GLHLP#8QWHUULFKW#YHUZHQGHW#ZHUGHQ1

² %HL#GHU#'DUVWHOOXQJ#YRQ#.UlIWHQ#PLW#3IHLOHQ# LVWZHVHQWOLFK/#GDVV#6FK�OHU#GLH#3IHLOOlQJH#DOV#$XVGUXFNGHV#%HWUDJHV#GHU#.UDIW#EHJUHLIHQ/#RKQH#PD�VWlEOLFKH'DUVWHOOXQJHQ#]XP#6HOEVW]ZHFN#ZHUGHQ#]X#ODVVHQ1

7DIHOELOG

7DIHOELOG

0|JOLFK# LVW# DXFK# GHU# 6HOEVWEDX# HLQHV#.UDIWPHV0VHUV#XQG#VHLQH#(LFKXQJ1#(LQ#VROFKHU#.UDIWPHVVHUNDQQ#DXFK#I�U#+DXVH[SHULPHQWH#YHUZHQGHW#ZHU0GHQ1

'DV# KRRNHVFKH# *HVHW]# +6(# /lQJHQlQGHUXQJ# HLQHU6FKUDXEHQIHGHU,# VROOWH# HUDUEHLWHW#ZHUGHQ/#ZHQQ# LP=XVDPPHQKDQJ#PLW# GHU#%HKDQGOXQJ#GHU#*HZLFKWV0NUDIW#JHNOlUW#LVW/#GDVV#GXUFK#+DNHQN|USHU#EHVWLPPWH*HZLFKWVNUlIWH#KHUYRUJHUXIHQ#ZHUGHQ1

'LH#.UDIW

'LH#.UDIW#JLEW#DQ/#ZLH#VWDUN#]ZHL#.|USHUDXIHLQDQGHU#HLQZLUNHQ1

#)RUPHO]HLFKHQ (LQKHLWHQ 'DUVWHOOXQJ

) 4#1HZWRQ#+41,4#N1# # 4#333#14#01# #4#333#333#1

%HWUDJ

$QJULIIVSXQNW 5LFKWXQJ

:LUNXQJHQ#YRQ#.UlIWHQ

.UlIWH#VLQG#QXU#DQ#LKUHQ#:LUNXQJHQ#HUNHQQEDU1

.UlIWH#N|QQHQ#KHUYRUUXIHQ

%HZHJXQJVlQGHUXQJHQ#YRQ#.|USHUQ

)RUPlQGHUXQJHQYRQ#.|USHUQ

bQGHUXQJ#GHU#*HVFKZLQGLJNHLW

bQGHUXQJ#GHU5LFKWXQJ#GHU%HZHJXQJ

SODVWLVFKH9HUIRUPXQJ

HODVWLVFKH9HUIRUPXQJ

=HUVW|UXQJGHV#.|USHUV

'LH#:LUNXQJ#HLQHU#.UDIW#LVW#DEKlQJLJ#YRQ#LKUHP#$QJULIIVSXQNW/#LKUHP#%HWUDJ#XQG#LKUHU#5LFKWXQJ1

Page 9: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

24

%HL#GHU#%HKDQGOXQJ#GHU#$UWHQ#YRQ#.UlIWHQ#JHKW#HVXP#HLQHQ#hEHUEOLFN1#9HUVFKLHGHQH#.UlIWH# VROOWHQ# LQLKUHU#:LUNXQJ#GHPRQVWULHUW#XQG# LP#hEHUEOLFN# FKD0UDNWHULVLHUW#ZHUGHQ1#'DEHL#LVW#]X#EHDFKWHQ/#GDVV#VLFKGLH# YHUVFKLHGHQHQ# .UlIWH# QLFKW# LQ# HLQH# EHVWLPPWH6\VWHPDWLN#HLQRUGQHQ#ODVVHQ#XQG#YRQ#LKUHP#&KDUDN0WHU#KHU#VHKU#XQWHUVFKLHGOLFK#VLQG1² 0DJQHWLVFKH#.UlIWH#DXI# IHUURPDJQHWLVFKH#.|U0SHU#+1lJHO/#6FKUDXEHQ/#%�URNODPPHUQ,#ODVVHQ#VLFKPLW#+LOIH# YRQ#3HUPDQHQW0# RGHU#(OHNWURPDJQHWHQGHPRQVWULHUHQ1

²# (OHNWULVFKH#.UlIWH#]HLJHQ#VLFK#]1 %1#EHLP#%DQG0JHQHUDWRU# +9HUlQGHUXQJ# GHU# /DJH# GHU#+ROXQGHU0PDUNN�JHOFKHQ#DXI#GHU#JUR�HQ#.XJHO,#RGHU#ZHQQPDQ# HLQHQ# JHODGHQHQ# .|USHU# LQ# GLH# 1lKH# YRQ3DSLHUVFKQLSVHOQ#RGHU#6W\URSRUN�JHOFKHQ#EULQJW1

²# $GKlVLRQVNUlIWH# DOV# .UlIWH# ]ZLVFKHQ# 7HLOFKHQYHUVFKLHGHQHU#6WRIIH#ODVVHQ#VLFK#JXW#PLW#+LOIH#YRQ]ZHL#*ODVSODWWHQ#GHPRQVWULHUHQ=#)HXFKWHW#PDQ#GLH2EHUIOlFKH#DQ/#VR#KDIWHQ#GLH#*ODVSODWWHQ#VHKU#JXWDXIHLQDQGHU#XQG# ODVVHQ#VLFK#QXU#P�KVDP#YRQHLQ0DQGHU#WUHQQHQ1

²# .RKlVLRQVNUlIWH# DOV# .UlIWH# ]ZLVFKHQ# 7HLOFKHQHLQHV#6WRIIHV#NDQQ#PDQ#JXW#PLW#+RO]VWlEHQ/#/LQHD0OHQ/#%ODWWIHGHUQ#RGHU#6WDWLYVWlEHQ#GHPRQVWULHUHQ1'DEHL# N|QQWH# PDQ# PLW# GHQ# 6FK�OHUQ# DXFK# GLHK\SRWKHWLVFKHQ#)UDJHQ#GLVNXWLHUHQ/#ZDV#SDVVLHUHQZ�UGH/#ZHQQ#HV#NHLQH#.RKlVLRQVNUlIWH#JlEH1

² $XI#GLH#*HZLFKWVNUDIW#XQG#GLH#5HLEXQJVNUDIWEUDXFKW#PDQ#DQ#GLHVHU#6WHOOH#QXU#]X#YHUZHLVHQ/#GDDXI#GLHVH#EHLGHQ#.UlIWH# LP#QDFKIROJHQGHQ#8QWHU0ULFKW#JHQDXHU#HLQJHJDQJHQ#ZLUG1

7DIHOELOG

,QVJHVDPW# VROOWH# GHQ# 6FK�OHUQ# GDEHL# GHXWOLFK# ZHU0GHQ/#GDVV#.|USHU#DXFK#DXIHLQDQGHU#ZLUNHQ/#ZHQQ#VLHVLFK#QLFKW# EHU�KUHQ# RGHU# GXUFK#6HLOH# RGHU#6WDQJHQPLWHLQDQGHU#YHUEXQGHQ#VLQG1

)�U#GLH#*HZLFKWVNUDIW#JLEW#HV#XQWHUVFKLHGOLFKH#0|J0OLFKNHLWHQ# GHU# YHUEDOHQ#'HILQLWLRQ>#ZREHL#PDQ# GDU0�EHU# KLQDXV# LQ# XQWHUVFKLHGOLFKHU#:HLVH# GLGDNWLVFKYHUHLQIDFKHQ#NDQQ=

41#9DULDQWH='LH#*HZLFKWVNUDIW#JLEW#DQ/#ZLH#VWDUN#HLQ#.|USHU#DXIHLQH# UXKHQGH#8QWHUODJH# GU�FNW# RGHU# DQ# HLQHU#$XI0KlQJXQJ#]LHKW1.RQVHTXHQ]HQ=#'LH#*HZLFKWVNUDIW#YHUlQGHUW#VLFK#PLW

EHVFKOHXQLJWHU#%HZHJXQJ#GHU#8QWHU0ODJH#RGHU#GHU#$XIKlQJXQJ1#'LH#*OHL0FKXQJ# )* P ü J JLOW# QXU# EHL# UX0KHQGHU# RGHU# JOHLFKI|UPLJ# EHZHJWHU8QWHUODJH#RGHU#$XIKlQJXQJ1

51#9DULDQWH='LH#*HZLFKWVNUDIW#JLEW#DQ/#ZLH#VWDUN#HLQ#.|USHU#YRQGHU#(UGH#DQJH]RJHQ#ZLUG1.RQVHTXHQ]HQ='LH#*OHLFKXQJ#)*# #P#ü#J#JLOW#XQHLQ0

JHVFKUlQNW1# 'LH# .UDIW# DXI# HLQHEHVFKOHXQLJW# EHZHJWH# 8QWHUODJH# LVWQLFKW# LGHQWLVFK# PLW# GHU# *HZLFKWV0NUDIW/#VLH#LVW#QXU#XQWHU#(LQEH]LHKXQJYRQ#7UlJKHLWVNUlIWHQ#IDVVEDU1

8P# GLH# 6FK�OHU# QLFKW# ]X# YHUZLUUHQ/# VROOWH# VLFK# GHU/HKUHU#DXI#HLQH#9DULDQWH#IHVWOHJHQ1

'LH#*HZLFKWVNUDIW

'LH#*HZLFKWVNUDIW#)*#JLEW#DQ/#ZLH#VWDUN#HLQ#.|USHU#DXI#HLQH#UXKHQGH#8QWHUODJH#GU�FNW#RGHU#DQ#HLQHU#$XIKlQJXQJ#]LHKW1

-H#JU|�HU#GLH#0DVVH#HLQHV#.|USHUV#LVW/#XP0VR#JU|�HU#LVW#VHLQH#*HZLFKWVNUDIW1

)*#aP

'LH#*HZLFKWVNUDIW#LVW#YRQ#GHP#2UW#DE0KlQJLJ/#DQ#GHP#VLFK#GHU#.|USHU#EHILQGHW1

)*/#0RQG ≈429#ü#)*/#(UGH

Page 10: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

25

9DULDQWH#4#NDQQ#GXUFK#HLQH#HLQIDFKH#([SHULPHQWLHU0IROJH#YHUGHXWOLFKW#ZHUGHQ=

,Q# GHQ# )lOOHQ# 6# XQG# 7# ]HLJW# GHU# .UDIWPHVVHU# HLQH.UDIW#+GLH#*HZLFKWVNUDIW,#DQ1

%HL#GHU#%HKDQGOXQJ#GHU#5HLEXQJVNUlIWH#DOV#EHZH0JXQJVKHPPHQGH#.UlIWH#VROOWH#DQ#GLH#6FK�OHU#GHU#I�UGLH#3UD[LV#ZLFKWLJH#*HGDQNH#KHUDQJHWUDJHQ#ZHUGHQ/GDVV#5HLEXQJVNUlIWH# HLQHUVHLWV# HUZ�QVFKW/# DQGHUHU0VHLWV#XQHUZ�QVFKW#VLQG1'LHVHU#*HGDQNH#NDQQ#DQ#%HLVSLHOHQ#DXV#GHP#(UIDK0UXQJVEHUHLFK#GHU#6FK�OHU#KHUDXVJHDUEHLWHW#ZHUGHQ=

² %HLP#)DKUUDG# LVW#GLH#+DIWUHLEXQJVNUDIW#]ZLVFKHQ6WUD�H# XQG#5HLIHQ# HUZ�QVFKW/# GLH#5HLEXQJVNUDIWLP#7UHWODJHU#XQHUZ�QVFKW1

² %HLP# $XWR# LVW# GLH# 5HLEXQJVNUDIW# ]ZLVFKHQ# 6WUD�HXQG#5HLIHQ#HLQHUVHLWV#HUZ�QVFKW#XQG#VROO#P|JOLFKVWJUR�#VHLQ#+]1 %1#]XP#VFKQHOOHQ#%UHPVHQ#HUIRUGHUOLFK,/DQGHUHUVHLWV#LVW#VLH#XQHUZ�QVFKW#XQG#VROO#NOHLQ#JHKDO0WHQ#ZHUGHQ#+HWZD#EHLP#)DKUHQ#DXI#JHUDGHU#6WUHFNH,1

² %HLP#)DKUHQ#PLW#GHP#6NDWHERDUG# RGHU#PLW#5ROO0VFKXKHQ# VROO# GLH# 5HLEXQJVNUDIW# NOHLQ# VHLQ/# EHLP$EEUHPVHQ#PXVV#VLH#JUR�#VHLQ1

9RQ#GDKHU#HUJLEW#VLFK#GLH#)UDJH/#ZRYRQ#GLH#5HLEXQJV0NUDIW#DEKlQJLJ# LVW1#'LH#8QWHUVXFKXQJHQ#GD]X#VROOWHQZHLWJHKHQG#LP#6FK�OHUH[SHULPHQW#HUIROJHQ/#QDFKGHPJHPHLQVDP#PLW#GHQ#6FK�OHUQ# JHNOlUW#ZXUGH/#ZHOFKH*U|�HQ2)DNWRUHQ#MHZHLOV#NRQVWDQW#JHKDOWHQ#RGHU#YDUL0LHUW#ZHUGHQ#N|QQHQ1#(LQH#$QOHLWXQJ# I�U#HLQH#H[SHUL0PHQWHOOH#8QWHUVXFKXQJ#LVW#LP#$+#61#9²:#HQWKDOWHQ1(V# NDQQ# DXFK# GDV# EHLOLHJHQGH#$UEHLWVEODWW# JHQXW]WZHUGHQ1# ,Q# LKP# LVW# HLQH# $QOHLWXQJ# I�U# HLQ# ([SHUL0PHQW#JHJHEHQ/#GDV#DOV#+DXVH[SHULPHQW#GXUFKJHI�KUWZHUGHQ#NDQQ1#,Q#$EKlQJLJNHLW#YRQ#GHU#.ODVVHQVLWXD0WLRQ#N|QQHQ#GHQ#6FK�OHUQ#ZHLWHUH#+LOIHQ#RGHU#DXFKHLQH#YHUN�U]WH#$QOHLWXQJ#JHJHEHQ#ZHUGHQ16lPWOLFKH#(UNHQQWQLVVH#ZHUGHQ# LQ# HLQHP#7DIHOELOGE]Z1#DXI#HLQHU#)ROLH#]XVDPPHQJHIDVVW1

=XU# )HVWLJXQJ# ELHWHW# HV# VLFK# DQ/#PLW# GHQ# 6FK�OHUQHLQLJH#)UDJHQ# ]X# HU|UWHUQ/#GLH# LKUHQ#(UIDKUXQJVEH0UHLFK#WDQJLHUHQ#XQG#DXFK#SUDNWLVFK#EHGHXWVDP#VLQG16ROFKH#)UDJHQ#VLQG#]1 %1=

² :LH#NDQQ#PDQ#EHL#HLQHP#)DKUUDG#GLH#EHZHJXQJV0KHPPHQGH# 5HLEXQJVNUDIW# ]ZLVFKHQ# 5HLIHQ# XQG6WUD�H#YHUULQJHUQ"

² %HL#HLQHP#$XWR#ZHUGHQ#%UHLWUHLIHQ#PRQWLHUW1#:HO0FKHQ#(LQIOXVV#KDW#GDV#DXI#GLH#5HLEXQJVNUDIW"

² %HL#.OHWW09HUVFKO�VVHQ/#ZLH#PDQ# VLH# EHL#6FKXKHQRGHU# 7DVFKHQ# ILQGHW/# ZLUG# GLH# 5HLEXQJ# JHQXW]W1:LH#HUUHLFKW#PDQ# LQ#GLHVHP#)DOOH#HLQH#JUR�H#5HL0EXQJVNUDIW"

² (LQH#VFKZHUH#.LVWH#VROO#YRQ#HLQHU#(FNH#GHV#5DXPHVLQ#HLQH#DQGHUH#(FNH#WUDQVSRUWLHUW#ZHUGHQ1#:HOFKH0|JOLFKNHLWHQ#JLEW#HV/#VLFK#GLHVH#$UEHLW#]X#HUOHLFK0WHUW"

² :LH#NDQQ#PDQ# HUUHLFKHQ/#GDVV#GHU#%UHPVZHJ#EHLHLQHP# )DKU]HXJ# +)DKUUDG/# $XWR,# P|JOLFKVW# NXU]LVW"#8QWHUVXFKXQJHQ#GD]X#N|QQHQ#]X#HLQHP#3UR0MHNW#DXVJHEDXW#ZHUGHQ1

=XU#=XVDPPHQIDVVXQJ#NDQQ#GDV#EHLOLHJHQGH#$UEHLWV0EODWW#JHQXW]W#ZHUGHQ/#LQ#GHP#ZLFKWLJH#(UNHQQWQLVVH]XVDPPHQJHIDVVW#VLQG1

,P# =XVDPPHQKDQJ# PLW# 5HLEXQJVNUlIWHQ# LP# 6WUD0�HQYHUNHKU#VROOWHQ#GHQ#6FK�OHUQ#DXFK#+LQZHLVH#]XP$%6#+$QWLEORFNLHUV\VWHP,#JHJHEHQ#ZHUGHQ1'DV#$%6#UHJHOW#EHL#HLQHU#9ROOEUHPVXQJ#GHQ#%UHPV0GUXFN#LQ#GHQ#HLQ]HOQHQ#%UHPV]\OLQGHUQ#LQ#$EKlQJLJ0NHLW# YRQ# GHU# 5DGYHU]|JHUXQJ# XQG# YHUKLQGHUW# GD0GXUFK#GDV#%ORFNLHUHQ#GHU#5lGHU1%HLP#$%6#ZHUGHQ#GLH#'UHK]DKOHQ#DOOHU#5lGHU#EHLP%UHPVHQ# VWlQGLJ# HOHNWURQLVFK# PLWHLQDQGHU# YHUJOL0FKHQ#XQG#GLH#]XU#RSWLPDOHQ#%UHPVXQJ#HUIRUGHUOLFKHQ:HUWH#GHV#%UHPVGUXFNV#HUPLWWHOW1(UJLEW#VLFK#HLQH#JU|�HUH#'LIIHUHQ]#LQ#GHQ#'UHK]DKOHQGHU# 5lGHU/# ]XP# %HLVSLHO# DOV# )ROJH# GHV# %ORFNLHUHQVHLQHV# 5DGHV# RGHU# PHKUHUHU# 5lGHU/# GDQQ# ZLUG# GLH%UHPVH#GLHVHU#5lGHU#VR#ODQJH#JHO|VW/#ELV#ZLHGHU#HWZDJOHLFKH# 'UHK]DKO# DOOHU# 5lGHU# HUUHLFKW# LVW1# 'LHVHU5HJHOSUR]HVV#HUIROJW#7#ELV#43#0DO#LQ#MHGHU#6HNXQGH1'DPLW#ZLUG#VWDWW#GHU#*OHLWUHLEXQJ#]ZLVFKHQ#5DG#XQG6WUD�H#ZLHGHU#GLH#+DIWUHLEXQJ#ZLUNVDP1#:HJHQ#GHUJU|�HUHQ# +DIWUHLEXQJVNUDIW# NDQQ# GDV# )DKU]HXJVLFKHU# DEJHEUHPVW# ZHUGHQ1# $XFK# 6HLWHQI�KUXQJV0NUlIWH#VLQG#ZLHGHU#ZLUNVDP1(V#VROOWH#EHWRQW#ZHUGHQ/#GDVV#$%6#QXU#EHL#9ROOEUHP0VXQJ#RGHU#EHL#*HIDKU#GHV#%ORFNLHUHQV#YRQ#5lGHUQ#DXI(LV#RGHU#6FKQHH#HLQH#5ROOH#VSLHOW1#)�U#GDV#%UHPVHQXQWHU#1RUPDOEHGLQJXQJHQ#KDW#HV#NHLQH#%HGHXWXQJ1(V#YHUKLQGHUW#DXFK#QLFKW#GDV#6FKOHXGHUQ#HLQHV#)DKU0]HXJHV#EHL#]X#VFKQHOOHU#.XUYHQIDKUW1#'DV#$%6#HUK|KW]ZDU# GLH# 9HUNHKUVVLFKHUKHLW/# ZLUG# DEHU# QXU# XQWHUVSH]LHOOHQ# %HGLQJXQJHQ# ZLUNVDP1# (V# HUVHW]W# QLFKWYRUDXVVFKDXHQGHV#XQG#YRUVLFKWLJHV#)DKUHQ1

Page 11: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

26

#$UEHLWVEODWW

.UlIWH#XQG#LKUH#:LUNXQJHQ

41 (UJlQ]H#GLH#hEHUVLFKW$:LUNXQJHQ#YRQ#.UlIWHQ

51 =HLFKQH#GLH#ZLUNHQGHQ#.UlIWH#HLQ$D, E, F,

61 :RYRQ#LVW#GLH#:LUNXQJ#HLQHU#.UDIW#DEKlQJLJ"

71 (UJlQ]H#GLH#hEHUVLFKW#]XU#5HLEXQJ$

bQGHUXQJ#GHU#%HZHJXQJ #

YRQ#.|USHUQ

%HLVSLHO= %HLVSLHO=#

$UW#GHU5HLEXQJVNUDIW

+DIWUHLEXQJVNUDIW

%HLVSLHOH# I�U# 1XW0]XQJ#GHU#5HLEXQJV0NUDIW

%HLVSLHOH# I�U# XQHU0Z�QVFKWHV# $XIWUH0WHQ

Page 12: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

27

#$UEHLWVEODWW

'LH#+DIWUHLEXQJ

(UPLWWOH#H[SHULPHQWHOO#GLH#+DIWUHLEXQJV]DKO#HLQHU#.HWWH/#GLH#DXI#HLQHP#7LVFK# OLHJW$#$OV+LOIVPLWWHO#VWHKW#GLU#QXU#HLQ#/LQHDO#]XU#9HUI�JXQJ1

9RUEHUHLWXQJ=

41 'LH# +DIWUHLEXQJV]DKO# ZLUG# QDFK# GHU# *OHL0FKXQJ# P # )5# 2# )4# EHUHFKQHW/# ZREHL# )5# GLH+DIWUHLEXQJVNUDIW#GHV#.HWWHQWHLOV# O4#XQG#)4GLH# *HZLFKWVNUDIW# GLHVHV# .HWWHQWHLOV# LVW18QWHU#ZHOFKHU#%HGLQJXQJ#EHJLQQW#GLH#.HWWH]X#JOHLWHQ"

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

51 %HJU�QGH/#GDVV#VLFK#GLH#+DIWUHLEXQJV]DKO#QDFK#GHU#*OHLFKXQJ#P# #O5#2#O4#EHUHFKQHQOlVVW$BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

BBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBBB

'XUFKI�KUXQJ=

41 %DXH#GLH#$QRUGQXQJ#HQWVSUHFKHQG#GHU#6NL]]H#DXI$51 9HUlQGHUH# GDV#9HUKlOWQLVV# YRQ# O4# ]X# O5# ODQJVDP/# ELV# GLH#.HWWH# JHUDGH# ]X# JOHLWHQEHJLQQW1%HVWLPPH#O4#XQG#O5#$#:LHGHUKROH#GLH#0HVVXQJHQ#PHKUPDOV$

61-)�KUH#GLH#0HVVXQJHQ#EHL#]ZHL#DQGHUHQ#/lQJHQ#GHU#.HWWH#GXUFK$

$XVZHUWXQJ=

0HVVXQJ1U1

#O4#LQ#FP

#O5#LQ#FP %HVWLPPH#GLH#+DIWUHLEXQJV]DKO$

6FKlW]H#GHQ#)HKOHU#GHV#(UJHEQLVVHV#DE$

Page 13: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

28

#.RSLHUYRUODJH

5HLEXQJVNUlIWHVLQG#.UlIWH#]ZLVFKHQ#]ZHL#.|USHUQ/#GLH#VLFK#EHU�KUHQ1#8UVDFKH#LVW#GLH#8QHEHQKHLWGHU#2EHUIOlFKHQ1

'LH#5HLEXQJVNUDIW#LVW#DEKlQJLJ

²#YRQ#GHU#.UDIW/#PLW#GHU#HLQ#.|USHU#DXI#VHLQH#8QWHUODJH#GU�FNW>²#YRQ#GHU#$UW#GHU#2EHUIOlFKH1

'LH#5HLEXQJVNUDIW#LVW#XQDEKlQJLJ#

²#YRQ#GHU#*U|�H#GHU#%HU�KUXQJVIOlFKHQ#GHU#EHLGHQ#.|USHU1

0HLVW#JLOW=#+DIWUHLEXQJVNUDIW#!#*OHLWUHLEXQJVNUDIW#!#5ROOUHLEXQJVNUDIW

'LH#5HLEXQJVNUDIW#NDQQ

YHUULQJHUW#ZHUGHQ #YHUJU|�HUW#ZHUGHQ#

+DIWUHLEXQJVNUDIW *OHLWUHLEXQJVNUDIW 5ROOUHLEXQJVNUDIWWULWW#DXI/#ZHQQ#HLQ#.|USHU#DXI#HLQHP#DQGHUHQ#UXKW1

WULWW#DXI/#ZHQQ#HLQ#.|USHU#DXI#HLQHP#DQGHUHQ#JOHLWHW1

WULWW#DXI/#ZHQQ#HLQ#.|USHU#DXI#HLQHP#DQGHUHQ#UROOW1

%HLVSLHO=.LVWH#VWHKW#DXI#GHP)X�ERGHQ1

%HLVSLHO=6NLIDKUHU#JOHLWHW#�EHU#GHQ#6FKQHH1

%HLVSLHO=$XWR#UROOW#DXI#HLQHU#6WUD�H1

² GXUFK#*OlWWHQ#GHU#2EHUIOlFKHQ/² GXUFK# 9HUNOHLQHUQ# GHU# .UDIW/PLW# GHU# HLQ# .|USHU# DXI# VHLQH8QWHUODJH#GU�FNW/

² GXUFK#6FKPLHUPLWWHO/² GXUFK#HLQ#Å/XIWNLVVHQ´1

² GXUFK#$XIUDXKHQ#GHU#2EHUIOlFKHQ/² GXUFK#9HUJU|�HUQ#GHU#.UDIW/#PLW#GHUHLQ# .|USHU# DXI# VHLQH# 8QWHUODJHGU�FNW1

Page 14: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kräfte und ihre Wirkungen

29

#.RSLHUYRUODJH

=XVDPPHQVHW]XQJ#YRQ#.UlIWHQ

:LUNHQ#]ZHL#.UlIWH#OlQJV#HLQHU#:LU0NXQJVOLQLH# LQ# JOHLFKHU# 5LFKWXQJ/# VRDGGLHUHQ#VLFK#LKUH#%HWUlJH1

:LUNHQ#]ZHL#.UlIWH#OlQJV#HLQHU#:LU0NXQJVOLQLH# LQ# HQWJHJHQJHVHW]WHU5LFKWXQJ/# VR# VXEWUDKLHUHQ# VLFK# LKUH%HWUlJH1

:LUNHQ#]ZHL#.UlIWH#VHQNUHFKW#]XHLQ0DQGHU# PLW# HLQHP# JHPHLQVDPHQ$QJULIIVSXQNW/# VR# HUJLEW# VLFK# GLHUHVXOWLHUHQGH#.UDIW#DXV#HLQHP#.UlI0WHSDUDOOHORJUDPP1

:LUNHQ# ]ZHL# .UlIWH# LQ# EHOLHELJHU5LFKWXQJ# PLW# HLQHP# JHPHLQVDPHQ$QJULIIVSXQNW/# VR# HUJLEW# VLFK# GLHUHVXOWLHUHQGH#.UDIW#DXV#HLQHP#.UlI0WHSDUDOOHORJUDPP1

Page 15: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Masse von Körpern und Dichte von Stoffen

30

71 41 6 0DVVH#YRQ#.|USHUQ#XQG#'LFKWH#YRQ6WRIIHQ

'LH#6FK�OHU#VROOHQ#GLH#*U|�HQ#0DVVH#XQG#*HZLFKWV0NUDIW#YRQHLQDQGHU#XQWHUVFKHLGHQ#N|QQHQ1#'LH#'LFKWHZLUG# DOV# 6WRIIHLJHQVFKDIW# HLQJHI�KUW/# ZREHL# I�U1LYHDX# ,,# DXFK# GLH# *OHLFKXQJ# ρ# #P29# EHKDQGHOWZLUG1'DUDXV# HUJHEHQ# VLFK# DOV# 8QWHUULFKWV]LHOH/# GDVV# GLH6FK�OHU² ZLVVHQ/#GDVV#MHGHU#.|USHU#HLQH#0DVVH#KDW#XQG#GLHVH0DVVH#XQDEKlQJLJ#GDYRQ# LVW/#ZR# VLFK#GHU#.|USHUEHILQGHW>

² GLH#0DVVH#YRQ#.|USHUQ#PLWWHOV#:DDJHQ#EHVWLPPHQN|QQHQ>

² 9RUVWHOOXQJHQ#�EHU#GLH#0DVVH#YHUVFKLHGHQHU#.|U0SHU#HQWZLFNHOQ>

² GHQ#=XVDPPHQKDQJ#]ZLVFKHQ#9ROXPHQ#XQG#0DVVHEHL#.|USHUQ#DXV#HLQHP#EHVWLPPWHQ#6WRII#HUIDVVHQ>

² GLH#SK\VLNDOLVFKH#%HGHXWXQJ#GHU#'LFKWH# DOV# VWRII0NHQQ]HLFKQHQGH#*U|�H#HUNHQQHQ>

² 'LFKWHQ#EHUHFKQHQ#N|QQHQ#XQG# LKQHQ#GLH#%HGHX0WXQJ#GHU#'LFKWH#YRQ#6WRIIHQ#LQ#GHU#3UD[LV#+%DXZH0VHQ/#7UDQVSRUWZHVHQ,#EHZXVVW#ZLUG1

0LW#GHU#0DVVH# OHUQHQ#GLH#6FK�OHU#QHEHQ#GHP#9ROX0PHQ#HLQH#]ZHLWH#.|USHUHLJHQVFKDIW#NHQQHQ1'LH# 6FK�OHU# YHUI�JHQ# EHUHLWV# �EHU# 9RUZLVVHQ=# 6LHZLVVHQ/# GDVV# YHUVFKLHGHQH# .|USHU# XQWHUVFKLHGOLFKVFKZHU#VLQG1#6LH#ZLVVHQ#DXFK/#GDVV#VLFK#YHUVFKLHGHQH.|USHU#XQWHUVFKLHGOLFK# VFKZHU# LQ#%HZHJXQJ# VHW]HQRGHU# DEEUHPVHQ# ODVVHQ1#$Q# DOOH# GLHVH#(UIDKUXQJHQNDQQ#PDQ#LP#8QWHUULFKW#DQNQ�SIHQ18QWHUVFKLHGOLFKH# 3RVLWLRQHQ# JLEW# HV# GDEHL# ]X# GHU)UDJH/# RE# PDQ# EHL# GHU# (LQI�KUXQJ# GHU# SK\VLNDOL0VFKHQ#*U|�H#0DVVH#GLH#6FKZHUH#RGHU#GLH#7UlJKHLW#LQGHQ# 9RUGHUJUXQG# VWHOOW# RGHU# EHLGH# $VSHNWH# HLQEH0]LHKW1)�U#GLH#6FK�OHU# LP#$QIDQJVXQWHUULFKW# HLQIDFKHU# ]XHUIDVVHQ# LVW# GLH# XQWHUVFKLHGOLFKH# 6FKZHUH# YRQ#.|U0SHUQ/#GLH# VHKU#DQVFKDXOLFK# YRQ#GHQ#6FK�OHUQ# VHOEVWGXUFK#$QKHEHQ#YHUVFKLHGHQHU#.|USHU#HUOHEW#ZHUGHQNDQQ1# 1LFKW# ]X# �EHUVHKHQ# LVW# GDEHL# DOOHUGLQJV# GLH*HIDKU# GHV# 'XUFKHLQDQGHUZHUIHQV# YRQ#0DVVH# XQG*HZLFKWVNUDIW1#'HVKDOE#LVW#]X#HPSIHKOHQ/#GHQ#$VSHNWGHU#7UlJKHLW# YRQ#.|USHUQ#PLW# HLQ]XEH]LHKHQ/# RKQHLKQ#DOOHUGLQJV#]X#YHUWLHIHQ1#'LHV# LVW#PLW#+LOIH#HLQID0FKHU#([SHULPHQWH#+$+#61#;,#P|JOLFK1

%HL#hEXQJHQ# ]XP#%HVWLPPHQ# GHU#0DVVH# YRQ#.|U0SHUQ#VROOWH#YRU#MHGHU#0HVVXQJ#LPPHU#HLQH#6FKlW]XQJVWHKHQ1#'DPLW#ZHUGHQ#QLFKW#QXU#*U|�HQYRUVWHOOXQ0JHQ# EHL# GHQ#6FK�OHUQ# HQWZLFNHOW/# VRQGHUQ# DXFK# GLH]ZHFNPl�LJH#$XVZDKO#YRQ#:DDJHQ#XQG#:lJHVlW]HQHUP|JOLFKW1#=XU#(QWZLFNOXQJ#YRQ#*U|�HQYRUVWHOOXQ0JHQ#NDQQ#DXFK#GLH#7DEHOOH#LP#/%#61#73#JHQXW]W#ZHU0GHQ1#*HUDGH# EHL#:DDJHQ# LVW# GLH# 7HQGHQ]# KLQ# ]X# GLJLWDODQ]HLJHQGHQ#:DJHQ# QLFKW# ]X# �EHUVHKHQ# XQG# VROOWHDXFK#LP#8QWHUULFKW#QLFKW#LJQRULHUW#ZHUGHQ1#

'LHVH#HOHNWURQLVFKHQ#:DDJHQ#+EHVVHU=#HOHNWURPHFKD0QLVFKH#:DDJHQ,#QXW]HQ# ]XU#:lJXQJ#PHLVW#GLH#:LU0NXQJ# GHU# *HZLFKWVNUDIW# GHV# .|USHUV# DXI# HLQHQ9HUIRUPXQJVN|USHU# +.UDIWPHVVGRVH#PLW# 'HKQXQJV0PHVVVWUHLIHQ#RGHU#)HGHU,#DXV1#'LH#:LGHUVWDQGVlQGH0UXQJ#GHU#'HKQXQJVPHVVVWUHLIHQ# LVW#GHU#9HUIRUPXQJSURSRUWLRQDO1# 'LH# /lQJHQlQGHUXQJ# HLQHU# )HGHUEHHLQIOXVVW#SURSRUWLRQDO#GLH#,QGXNWLYLWlW#HLQHU#6SXOHRGHU#GLH#.DSD]LWlW# HLQHV#.RQGHQVDWRUV1#0DQ# HUKlOWDOVR# DOV#0HVVJU|�H# HLQH# HOHNWULVFKH# 6SDQQXQJ/# GLHGHU#*HZLFKWVNUDIW#XQG#GDPLW#QDFK#)*# #P# ü# J#GHU0DVVH# SURSRUWLRQDO# LVW# XQG# QDFK# HQWVSUHFKHQGHU8PIRUPXQJ#GLJLWDO#RGHU#DQDORJ#DQJH]HLJW#ZLUG1(LQH#%HKDQGOXQJ#GHV#0HVVSULQ]LSV#�EHUVWHLJW#DOOHU0GLQJV#GLH#0|JOLFKNHLWHQ#GHV#$QIDQJVXQWHUULFKWV1

'LH#8QWHUVFKLHGH# GHU#*HZLFKWVNUlIWH# YRQ# .|USHUQJOHLFKHU#0DVVH# DQ# YHUVFKLHGHQHQ#2UWHQ# NDQQ# HU|U0WHUW# ZHUGHQ1# 'DYRQ# DXVJHKHQG# NDQQ# GLH# 8QWHUVX0FKXQJ#GHV#=XVDPPHQKDQJV#]ZLVFKHQ#*HZLFKWVNUDIWXQG#0DVVH#GXUFK#HLQ#([SHULPHQW#HUIROJHQ/#DXV#GHPGHU#2UWVIDNWRU#DOV#3URSRUWLRQDOLWlWVIDNWRU#JHZRQQHQZLUG#+$+#61#<,1#$XV#GLHVHP#([SHULPHQW#ZHUGHQ#DXFKGLH#+DNHQN|USHU#DOV#I�U#GLH#(U]HXJXQJ#YRQ#EHVWLPP0WHQ#*HZLFKWVNUlIWHQ#JHHLJQHW#YHUVWDQGHQ1#'LH#8QWHUVFKHLGXQJ# YRQ#0DVVH# XQG#*HZLFKWVNUDIWIlOOW#YLHOHQ#6FK�OHUQ#VFKZHU1#(LQH#*HJHQ�EHUVWHOOXQJ+V1#/%#61#74,#NDQQ#KHOIHQ/#GDVV#GLH#6FK�OHU#EHLGH#*U|0�HQ#EHVVHU#YRQHLQDQGHU#DEJUHQ]HQ#N|QQHQ1'DEHL# VROOWHQ# GLH# 6FK�OHU# DXFK# GDUDXI# DXIPHUNVDPJHPDFKW#ZHUGHQ/#GDVV#LQ#%HGLHQXQJVDQOHLWXQJHQ#YRQWHFKQLVFKHQ#*HUlWHQ# LQ#GHU#5HJHO#GDV#*HZLFKW# LQ#JRGHU#NJ#DQJHJHEHQ#ZLUG1#'LHV#HQWVSULFKW#GHQ# LQ#GHU7HFKQLN#J�OWLJHQ#1RUPHQ#XQG# LVW#NHLQ#:LGHUVSUXFK]X#',10(PSIHKOXQJHQ1

Page 16: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Masse von Körpern und Dichte von Stoffen

31

7DIHOELOG

9LHOH# 6FK�OHU# YHUELQGHQ# GHQ# %HJULII# 0DVVH# PLWVFKZHUHQ#.|USHUQ1#(V# IlOOW# LKQHQ# VFKZHU#]X#HUNHQ0QHQ/#GDVV#DXFK#OHLFKWH#.|USHU#+ELV#KLQ#]XU#/XIW,#HLQH0DVVH#KDEHQ1

8P#)HKOYRUVWHOOXQJHQ#HQWJHJHQ]XZLUNHQ/#LVW#HV#GHV0KDOE#]ZHFNPl�LJ/#PLW#GHQ#6FK�OHUQ#DXFK#VROFKH#)UD0JHQ#ZLH² +DEHQ#DXFK#HLQ#%ODWW#3DSLHU/#HLQH#)HGHU/#HLQ#+DDUHLQH#0DVVH"#:LH#NDQQ#PDQ#VLH#EHVWLPPHQ"

² +DW#DXFK#GLH#/XIW#LQ#HLQHP#*HIl�#HLQH#0DVVH"]X#NOlUHQ1

'LH# ]XOHW]W# JHQDQQWH#)UDJH# LVW# LP#/%#61# 78# GDUJH0VWHOOW1%HL# GHU# H[SHULPHQWHOOHQ# 5HDOLVLHUXQJ# LVW# 9RUVLFKWJHERWHQ1# %HL# ]X# VWDUNHU# 9HUULQJHUXQJ# GHV# 'UXFNHVRGHU#XQJHHLJQHWHQ#*HIl�HQ#EHVWHKW#,PSORVLRQVJHIDKU1,QZLHZHLW# DXI# GLH# 7UlJKHLW# YRQ# .|USHUQ# DQ# GLHVHU6WHOOH#RGHU# LP#=XVDPPHQKDQJ#PLW#GHU#%HKDQGOXQJYRQ#%HZHJXQJHQ#HLQJHJDQJHQ#ZLUG/#REOLHJW#GHU#(QW0VFKHLGXQJ#GHV#/HKUHUV1#(V#VHL#DEHU#GDUDXI#DXIPHUN0VDP# JHPDFKW/# GDVV# JHUDGH# GLH# 7UlJKHLW# LP6WUD�HQYHUNHKU# I�U# YLHOH# 6FK�OHU# YRQ# ,QWHUHVVH# LVW1'D]X# NDQQ# GLH# EHLOLHJHQGH# .RSLHUYRUODJH# JHQXW]WZHUGHQ/#XP#PLW#GHQ#6FK�OHUQ#�EHU#GLH#7UlJKHLW#YRQ.|USHUQ#LP#6WUD�HQYHUNHKU#]X#GLVNXWLHUHQ1

)�U# GLH# (LQI�KUXQJ# GHU# 'LFKWH# KDW# VLFK# GHU# LP/% 61 76#VNL]]LHUWH#:HJ#EHZlKUW1

² 'HQ#6FK�OHUQ#ZLUG#DQ#%HLVSLHOHQ#YHUGHXWOLFKW/#GDVV.|USHU#JOHLFKHQ#9ROXPHQV#XQWHUVFKLHGOLFKH#0DVVHKDEHQ# N|QQHQ1# 'DV# OlVVW# VLFK# PLW# +LOIH# HLQHU:DDJH# XQG# YHUVFKLHGHQHU# .|USHU# JOHLFKHQ# 9ROX0PHQV# ++RO]NORW]#XQG#6W\URSRUN|USHU/#:DVVHU#XQG6SLULWXV,#JXW#]HLJHQ1

² 'HQ#6FK�OHUQ#ZLUG#ZHLWHU#YHUGHXWOLFKW/#GDVV#.|U0SHU# XQWHUVFKLHGOLFKHQ# 9ROXPHQV# JOHLFKH# 0DVVHKDEHQ#N|QQHQ1#'D]X#ELHWHW#GHU#8QWHUULFKWVPLWWHO0KDQGHO#HLQHQ#HQWVSUHFKHQGHQ#6DW]#YRQ#.|USHUQ#DQ+V1#/%#61# 7626,1#0DQ#NDQQ#VLFK#DXFK#VHOEVW#HLQLJHVROFKHU#.|USHU#DQIHUWLJHQ1

$XV# GLHVHQ#%HWUDFKWXQJHQ# HUJLEW# VLFK=#(V#EHVWHKHQ=XVDPPHQKlQJH#]ZLVFKHQ#GHU#0DVVH/#GHP#9ROXPHQXQG#GHP#6WRII/#DXV#GHP#HLQ#.|USHU#EHVWHKW1'LHVH# =XVDPPHQKlQJH# N|QQHQ# QXQ# I�U# PHKUHUH.|USHU# DXV# MHZHLOV# HLQHP# 6WRII# XQWHUVXFKW#ZHUGHQ+]1 %1#I�U#:DVVHU#LP#%HFKHUJODV#DXI#HLQHU#:DDJH/#I�UPHKUHUH#JOHLFK#JUR�H#+RO]N|USHU/#I�U#PHKUHUH#JOHLFKJUR�H#6W\URSRUZ�UIHO1#'DV#NDQQ# WHLOZHLVH# LP#+DXV0H[SHULPHQW#JHVFKHKHQ1#'D]X#ELHWHW#GDV#$+#61#4<#HLQH([SHULPHQWLHUDQOHLWXQJ1#'DEHL#HUKlOW#PDQ=

'LH#0DVVH#YRQ#.|USHUQ

'LH#0DVVH#JLEW#DQ/#ZLH#VFKZHU#RGHU#ZLH#OHLFKW#HLQ#.|USHU#LVW1#6LH#LVW#I�U#HLQHQ#EHVWLPP0WHQ#.|USHU#�EHUDOO#JOHLFK#JUR�1

)RUPHO]HLFKHQ (LQKHLWHQ 0HVVJHUlWH

P 4#NJ# 4#333#J4#J# 4#333#PJ4#W 4#333#NJ

:DDJHQ#+%ULHIZDDJH/#3HUVRQHQ0ZDDJH/#HOHNWURQLVFKH#:DDJH,

9HUVFKLHGHQH# .|USHU# VLQGXQWHUVFKLHGOLFK# VFKZHU1# 6LHZHUGHQ# YRQ# GHU# (UGH# XQWHU0VFKLHGOLFK#VWDUN#DQJH]RJHQ1

Page 17: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Masse von Körpern und Dichte von Stoffen

32

² )�U#.|USHU#DXV#HLQ#XQG#GHPVHOEHQ#6WRII#JLOW=#9HU0GRSSHOW# +YHUGUHLIDFKW,#PDQ# GDV#9ROXPHQ/# VR# YHU0GRSSHOW#+YHUGUHLIDFKW,#VLFK#GLH#0DVVH#GHV#.|USHUV19HUDOOJHPHLQHUW#JLOW=#P#a91

² 'HU#4XRWLHQW#P# =#9# LVW# I�U# EHOLHELJH#.|USHU# DXVHLQHP#EHVWLPPWHQ#6WRII#MHZHLOV#JOHLFK1#(U#ZLUG#DOV'LFKWH#GHV#6WRIIHV#EH]HLFKQHW1

)�U#GLH#ZHLWHUH#)HVWLJXQJ#ELHWHQ#/%#+61#7< ² 83,#XQG$+# +61# ; ²44,# ]DKOUHLFKH#$QUHJXQJHQ1#6FKZHUSXQNWHVROOWHQ#GDEHL#VHLQ=² 'LH# ,QWHUSUHWDWLRQ# GHU# 'LFKWH# YRQ# 6WRIIHQ1# (LQH$XVZDKO#ILQGHW#GHU#/HKUHU#LP#/%/#ZHLWHUH#'LFKWHQ]1#%1#LQ#GHQ#3$(7(&07DIHOZHUNHQ1

² 'LH#%HVWLPPXQJ#GHU#'LFKWH#HLQHV#6WRIIHV#XQG#GDU0DXV#GLH#(UPLWWOXQJ#GHV#6WRIIHV/#DXV#GHP#GHU#.|U0SHU# EHVWHKW1# %HL# VROFKHQ# ([SHULPHQWHQ# ZLUG]XJOHLFK#GDV#%HVWLPPHQ#YRQ#0DVVH#XQG#9ROXPHQZLHGHUKROW#XQG#GDPLW#JHIHVWLJW1

² %HUHFKQXQJHQ#YRQ#'LFKWHQ/#9ROXPHQ#XQG#0DVVHQ+$+#61#44/#/%#61#7< ² 83,1

'LH#6FK�OHU#N|QQHQ#DXFK#GD]X#DQJHUHJW#ZHUGHQ/#VLFKHLQHQ#HLQIDFKHQ#'LFKWHPHVVHU#+$UlRPHWHU,#VHOEVW#]XEDXHQ# +V1#QHEHQVWHKHQGH#6NL]]H,1#'D]X#ZLUG# LQ#GHQ'HFNHO#HLQHV#QLFKW#]X#NOHLQHQ#7DEOHWWHQU|KUFKHQV#HLQ7ULQNKDOP#HLQJHNOHEW#XQG#LQ#GDV#7DEOHWWHQU|KUFKHQNOHLQH# 1lJHO# RGHU# 6FKUDXEHQ# ]XP# $XVWDULHUHQJHEUDFKW1

7DIHOELOG

'LH#(LQWDXFKWLHIH# LQ#/HLWXQJVZDVVHU#ZLUG#PDUNLHUWXQG#PLW#GHU#(LQWDXFKWLHIH#LQ#6DO]ZDVVHU/#(VVLJ/#6SLUL0WXV#XQG#DQGHUHQ#)O�VVLJNHLWHQ#YHUJOLFKHQ1

=X# HLQHU#*HVDPW]XVDPPHQIDVVXQJ# HLJQHW# VLFK# GDVEHLOLHJHQGH# $UEHLWVEODWW/# GDV# GLH# 6FK�OHU# HUJlQ]HQXQG#LQ#LKUH#8QWHUODJHQ#HLQKHIWHQ#N|QQHQ1

'LH#'LFKWH#YRQ#6WRIIHQ

'LH#'LFKWH#JLEW#DQ/#ZHOFKH#0DVVH# MHGHU#.XELN]HQWLPHWHU#9ROXPHQ#HLQHV#6WRIIHV#KDW1#6LHNHQQ]HLFKQHW#GHQ#6WRII/#DXV#GHP#HLQ#.|USHU#EHVWHKW1

'LH#'LFKWH#NDQQ#DXV#0DVVH#XQG#9ROXPHQ#EHUHFKQHW#ZHUGHQ1#'LH#'LFKWH#YRQ#)O�VVLJNHLWHQNDQQ#PDQ#PLW#$UlRPHWHUQ#PHVVHQ1

'LFKWH 0DVVH#GHV#.|USHUV9ROXPHQ#GHV#.|USHUV00000000000000000000000000000000000000000000000000000000000

U P900000

(LQKHLWHQ=

1 NJP6000000000 1

J

O000 0 001

JFP6000000000000,

4 JFP6000000000000 4 NJ

GP60000000000000 4333 NJ

P6000000000

Page 18: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Masse von Körpern und Dichte von Stoffen

33

#.RSLHUYRUODJH

Page 19: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Masse von Körpern und Dichte von Stoffen

34

#$UEHLWVEODWW

(LJHQVFKDIWHQ#YRQ#.|USHUQ

51#-HGHU#.|USHU#QLPPW#HLQHQ#5DXP#HLQ1#(U#KDW#HLQ#9ROXPHQ#91#(V#NDQQ#HUPLWWHOW#ZHUGHQ1

61#)RUP#XQG#9ROXPHQ#YRQ#.|USHUQ#VLQG#YRQ#GHU#$UW#GHU#.|USHU#DEKlQJLJ1

71#-HGHU#.|USHU#KDW#HLQH#0DVVH#P1#'LH#0DVVH#ZLUG#PLW# #JHPHVVHQ1

(LQKHLWHQ#GHU#0DVVH=#

81#-HGHU#.|USHU#EHVWHKW#DXV#6WRII/#XQG#MHGHU#6WRII#KDW#HLQH#EHVWLPPWH#'LFKWH1

²#IHVW %HLVSLHO=

41#.|USHU#N|QQHQ#VHLQ= ²# %HLVSLHO=

²# %HLVSLHO=

EHL#UHJHOPl�LJ#JHIRUPWHQ#.|USHUQ#GXUFK#/lQJHQPHVVXQJ#XQG#%HUHFKQXQJ

EHL#XQUHJHOPl�LJ#JHIRUPWHQ#.|U0SHUQ#PLW#+LOIH#YRQ#0HVV]\OLQGHUQ

IHVWH#.|USHU )O�VVLJNHLWHQ *DVH

)RUP EHVWLPPWH#)RUP

9ROXPHQ EHVWLPPWHV#9ROXPHQ

4#NJ J 4#J# # PJ 4#W# NJ

9# #9# #

'LFKWH 0DVVH#GHV#.|USHUV9ROXPHQ#GHV#.|USHUV00000000000000000000000000000000000000000000000000000000000 U# #

Page 20: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

35

71 41 7 .UDIWXPIRUPHQGH#(LQULFKWXQJHQ

,P#0LWWHOSXQNW#GLHVHV#$EVFKQLWWHV#VWHKHQ#GLH#.UDIW0XPZDQGOXQJ# PLWWHOV# 5ROOHQ# XQG# +HEHO# VRZLH# GLH$QZHQGXQJ#GHV#+HEHOJHVHW]HV1'HU#ZHVHQWOLFKH#8QWHUVFKLHG#]ZLVFKHQ#1LYHDX#,#XQG,,#EHVWHKW#GDULQ/#GDVV#EHL#1LYHDX#,#HLQH#SKlQRPHQR0ORJLVFKH#%HWUDFKWXQJVZHLVH#GRPLQLHUW/#EHL#1LYHDX#,,GDJHJHQ#GLH# TXDQWLWDWLYHQ#=XVDPPHQKlQJH# VWlUNHUEHWRQW#ZHUGHQ15ROOHQ#NHQQHQ#GLH#6FK�OHU#]XPHLVW#VFKRQ#DXV#LKUHP(UIDKUXQJVEHUHLFK/# ]1%1# YRQ# .UDQHQ/# )ODVFKHQ]�0JHQ/#$XI]�JHQ/#6SDQQYRUULFKWXQJHQ#I�U#)DKUGUlKWH1(V#NRPPW#QXQ#GDUDXI#DQ/#HLQH#6\VWHPDWLVLHUXQJ#YRU0]XQHKPHQ#XQG#VFKRQ#PLW#%OLFN#DXI#GLH#)RUPXOLHUXQJGHU#*ROGHQHQ#5HJHO#GHU#0HFKDQLN#$XVVDJHQ#]X#.UlI0WHQ#XQG#:HJHQ#]X#IRUPXOLHUHQ1(LQEH]RJHQ#ZHUGHQ#VROOWHQ#DXI#MHGHQ#)DOO#6FK�OHUH[0SHULPHQWH1#,P#$+#61#45#LVW#GD]X#HLQH#([SHULPHQWLHU0DQOHLWXQJ#I�U#GLH#ORVH#5ROOH#HQWKDOWHQ1(QWVSUHFKHQGH#8QWHUVXFKXQJHQ#VLQG#DXFK#EHL#HLQHUIHVWHQ#5ROOH#GXUFK]XI�KUHQ1#'D]X#HLJQHW#VLFK#GDV#EHL0OLHJHQGH#$UEHLWVEODWW1)�U# GLH#([SHULPHQWH# ]XP#9HUJOHLFK# GHU#$UEHLW# DQ5ROOHQ#NDQQ#GDV#/LQHDO#DOV#6WDWLY#EHQXW]W#ZHUGHQ/ZHQQ# DP# (QGH# 70PP0%RKUXQJHQ# ]XP# (LQVWHFNHQGHV#5ROOHQ]DSIHQV#JHERKUW#ZHUGHQ19HUVFKLHGHQH#+XEK|KHQ#ODVVHQ#UHDOLVLHUHQ/#ZHQQ#GLH/DVW#DXI#GHQ#+RO]NORW]#JHKREHQ#ZHUGHQ#VROO/#GHU# LQGUHL#YHUVFKLHGHQHQ#/DJHQ#DXIJHVWHOOW#ZLUG1

$OV#HLQH#(UNXQGXQJVDXIJDEH#ELHWHW#HV# VLFK#DQ/#GDVVGLH#6FK�OHU#KHUDXVILQGHQ/#ZLH#GLH#5ROOHQ#]XP#6SDQ0QHQ#YRQ#)DKUGUlKWHQ#EHL#HOHNWULIL]LHUWHQ#(LVHQEDKQ0VWUHFNHQ#RGHU#EHL#GHU#6WUD�HQEDKQ#DQJHRUGQHW#VLQG1'LH#LP#/%#61#8;#REHQ#EHVFKULHEHQH#YHUHLQIDFKWH#XQGGDPLW# I�U# GHQ# 6FK�OHU# JXW# �EHUVFKDXEDUH#9DULDQWHLVW#]XPHLVW#HUVHW]W#GXUFK#HLQH#.RPELQDWLRQ#YRQ#ORVHU5ROOH#XQG#6WXIHQUROOH#+:HOOUDG/#V1#6NL]]H,1

,Q# OHLVWXQJVVWDUNHQ#.ODVVHQ# NDQQ# DXFK# GLHVH# 9DUL0DQWH#HU|UWHUW#ZHUGHQ1

$OV#ZHLWHUH#(UNXQGXQJVDXIJDEH#N|QQHQ#GLH#6FK�OHUEHDXIWUDJW#ZHUGHQ/#GHQ#$XIEDX#HLQHV#7XUPGUHKNUD0QHV# ]X# EHREDFKWHQ# XQG# ]X# VNL]]LHUHQ1# (LQH# VROFKH$XIJDEH# NDQQ# XQWHUVHW]W# ZHUGHQ# PLW# )UDJHQ# ZLH]1 %1=

² :LH#YHUOlXIW#GDV#6HLO/#PLW#GHP#GHU#+DNHQ#JHKREHQZLUG"=HLFKQH# GHQ# 9HUODXI# GHV# 6HLOV# XQG# GLH# 5ROOHQ# LQHLQH#6NL]]H#GHV#.UDQHV#HLQ$

² :LH#YLHO#6HLOH#WUDJHQ#GHQ#+DNHQ"² :LH#ZLUG#GHU#:DJHQ#DP#.UDQDXVOHJHU#YHUVFKREHQ"6NL]]LHUH#DXFK#GDV$

² 6XFKH#DP#.UDQDXVOHJHU#6FKLOGHU1#*LE#LQ#GHU#6NL]]HDQ/#ZR#GLH#6FKLOGHU#XQJHIlKU#DQJHEUDFKW#VLQG#XQGQRWLHUH/#ZDV#DXI#GHQ#6FKLOGHUQ#VWHKW$

'LH#6FK�OHU#N|QQHQ#DXFK#GD]X#DQJHUHJW#ZHUGHQ/#VLFK]X#+DXVH#DXV#6FKO�VVHOULQJHQ#XQG#%LQGIDGHQ#HLQID0FKH#$QRUGQXQJHQ#]XVDPPHQ]XEDXHQ#XQG#8QWHUVX0FKXQJHQ#GXUFK]XI�KUHQ1

IHVWH#5ROOH# #ORVH#5ROOH# #)ODVFKHQ]XJ

hEHU]HXJHQG#LVW#I�U#6FK�OHU#DXFK#IROJHQGHU#9HUVXFK=8P#]ZHL#6WDQJHQ#ZLUG#PHKUIDFK#HLQ#6HLO#JHVFKOXQ0JHQ1#=ZHL#NUlIWLJH#6FK�OHU#YHUVXFKHQ#GLH#6WDQJHQ#LQLKUHU#/DJH#]X#KDOWHQ/#ZlKUHQG#HLQ#QLFKW#VR#NUlIWLJHU6FK�OHU#DQ#GHP#6HLO#]LHKW1(LQH#(UNOlUXQJ#I�U#GHQ#(IIHNW#NDQQ#�EHU#GLH#$Q]DKOGHU#ÅWUDJHQGHQ´#6HLOH#JHJHEHQ#ZHUGHQ1

Page 21: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

36

)�U#GLH#6FK�OHU#VHKU#DQVFKDXOLFK#VLQG#'HPRQVWUDWL0RQVH[SHULPHQWH# LQ# HLQHP# YHUWLNDOHQ# 9HUVXFKVDXI0EDX1# 'D]X# HLJQHW# VLFK# HLQH# 0DQLSHUP0+DIWWDIHO1'DPLW# LVW# HV# P|JOLFK/# $SSOLNDWLRQHQ# +]1%1# .UDIW0SIHLOH,#]X#QXW]HQ#RGHU#DQ#GHU#7DIHO#]X#]HLFKQHQ#E]Z1]X#VFKUHLEHQ1

:LUG#GLH#7DIHO#VWDELO#DXI#HLQHP#5ROOWLVFK#EHIHVWLJW/#VRVLQG# GLH# =XJULIIV0# XQG# 7UDQVSRUWEHGLQJXQJHQ# RSWL0PDO#JHO|VW1

'LH#%HIHVWLJXQJ#HUIROJW#DP#5DKPHQ#GHU#7DIHO#PLWWHOV7LVFKNOHPPHQ/#LQ#GLH#6WDWLYVWlEH#]XU#$XIQDKPH#GHU5ROOHQ/#)HGHUNUDIWPHVVHU#XQG#DQGHUHU#7HLOH#JHVWHFNWZHUGHQ1#0LW#6WHOOULQJHQ#E]Z1#5LQJHQ#PLW#+DNHQ#ZHU0GHQ#GLH#DQJHEUDFKWHQ#7HLOH#JHVLFKHUW#+V1#6NL]]H,1

ZHUGHQ1#0LW#6WHOOULQJHQ#E]Z1#5LQJHQ#PLW#+DNHQ#ZHU0GHQ#GLH#DQJHEUDFKWHQ#7HLOH#JHVLFKHUW#+V1#6NL]]H,1

7LVFKNOHPPH#PLW#6WDWLYVWDE#XQG#5LQJ#PLW#+DNHQ#DP5DQG# GHU#7DIHO#EHIHVWLJW# JHEHQ#GLH#0|JOLFKNHLW#GHU+DOWHUXQJ#YRQ#)HGHUNUDIWPHVVHUQ1

0LW# GLHVHP# VWDELOHQ# 9HUVXFKVDXIEDX# N|QQHQDQVFKDXOLFK#]XU#%HKDQGOXQJ#NUDIWXPIRUPHQGHU#(LQ0ULFKWXQJHQ#.UlIWH#ELV#]X#433#1#ZLUNHQ#XQG#JHVWDWWHQGDPLW#�EHU]HXJHQGH#SK\VLNDOLVFKH#([SHULPHQWH1

'LH#=HLFKQXQJ#YHUGHXWOLFKW#GLH#0|JOLFKNHLW#YHUWLND0OHU#'HPRQVWUDWLRQVWHFKQLN#]X#GLHVHP#6WRIIJHELHW1

Page 22: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

37

#$UEHLWVEODWW

.UlIWH#XQG#:HJH#DQ#5ROOHQ

$XIJDEH=9HUJOHLFKH#DQ#HLQHU#IHVWHQ#5ROOH#XQG#DQ#HLQHU#ORVHQ#5ROOH#GLH#.UlIWH/#GLH#]XU�FNJHOHJWHQ:HJH#XQG#GLH#YHUULFKWHWHQ#PHFKDQLVFKHQ#$UEHLWHQ#DQ#GHU#/DVW#PLW#GHQHQ/#GLH#DP#IUHLHQ6HLOHQGH#HUPLWWHOW#ZHUGHQ1

'XUFKI�KUXQJ=41 D,%DXH#GLH#([SHULPHQWLHUDQRUGQXQJ#D,#I�U#HLQH

IHVWH#5ROOH#DXI$E,%HVWLPPH# GLH#.UDIW#)+# ]XP#+HEHQ#GHU#/DVWRKQH#5ROOH$

F,0LVV#GLH#=XJNUDIW#)=#DP#6HLOHQGH#EHLP#+HEHQGHU#/DVW$

G,%HVWLPPH# GHQ# +XEZHJ# V+# EHLP# +HEHQ# GHU/DVW# DXI# GHQ#.ORW]# XQG# GHQ# HQWVSUHFKHQGHQ=XJZHJ#V=#DP#6HLOHQGH$

51 D,%DXH#GLH#([SHULPHQWLHUDQRUGQXQJ#E,#I�U#HLQH#ORVH#5ROOH#DXI$E,%HVWLPPH#GLH#.UDIW#)=#]XP#+HEHQ#GHU#/DVW#RKQH#5ROOH/#LQGHP#GX#EHLGH#6HLOHQGHQ#DQGHQ#)HGHUNUDIWPHVVHU#KlQJVW$

F,0LVV#GLH#=XJNUDIW#)=#DP#6HLOHQGH#EHLP#+HEHQ#GHU#/DVW$G,%HVWLPPH#GHQ#+XEZHJ#V+#EHLP#+HEHQ#GHU#/DVW#DXI#GHQ#.ORW]#XQG#GHQ#HQWVSUHFKHQ0GHQ#=XJZHJ#V=#DP#6HLOHQGH$

$XVZHUWXQJ=IHVWH#5ROOH ORVH#5ROOH

D, 9HUJOHLFKH#EHL#EHLGHQ#5ROOHQ#MHZHLOV#=XJNUDIW#XQG#+XENUDIW$

E, 9HUJOHLFKH#EHL#EHLGHQ#5ROOHQ#MHZHLOV#=XJZHJ#XQG#+XEZHJ$

F, :LH#YHUlQGHUW#VLFK#GHU#=XJZHJ/#ZHQQ#.UDIW#HLQJHVSDUW#ZLUG"

)+ )=# #V+ #V= )+ )=# #V+ #V=

IHVWH#5ROOH= ORVH#5ROOH=

IHVWH#5ROOH= ORVH#5ROOH=

Page 23: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

38

$Q# ]DKOUHLFKHQ# %HLVSLHOHQ# DXV# GHP# $OOWDJVOHEHQVROOWH# GHQ# 6FK�OHUQ# EHZXVVW# JHPDFKW#ZHUGHQ/# GDVV+HEHO# LQ#HLQHU#9LHO]DKO#YRQ#)RUPHQ#H[LVWLHUHQ#XQGZLU#VWlQGLJ#PLW#+HEHOQ#XPJHKHQ# +=DQJHQ/#6FKHUHQ/)ODVFKHQ|IIQHU/#7�UNOLQNHQ#XVZ1,1#(LQH# LQWHUHVVDQWH$XIJDEH#I�U#6FK�OHU#LVW#HV#DXFK#]X#HUNXQGHQ/#ZR#VLFKLP#.ODVVHQUDXP#E]Z1#]X#+DXVH#+HEHO#EHILQGHQ1#(LQVHKU#ÅHUJLHELJHV´#2EMHNW#I�U#HLQH#VROFKH#(UNXQGXQJLVW#GDV#)DKUUDG1

'LHVH#Å6LFKWXQJ´#YRQ#+HEHOQ#XQWHUVFKLHGOLFKHU#$UWNDQQ#]XJOHLFK#JHQXW]W#ZHUGHQ/#XP#HLQH#(LQWHLOXQJ#LQHLQVHLWLJH#XQG#]ZHLVHLWLJH#+HEHO#YRU]XQHKPHQ1'DV#ZHLWHUH#+HUDQJHKHQ#NDQQ# LQ#XQWHUVFKLHGOLFKHU:HLVH#HUIROJHQ=(LQH#0|JOLFKNHLW# EHVWHKW#GDULQ/# GLH#)UDJH#QDFK# GHP*OHLFKJHZLFKW#DP#+HEHO#LQ#GHQ#0LWWHOSXQNW#]X#VWHOOHQ1'LH# H[SHULPHQWHOOH# 8QWHUVXFKXQJ# GD]X# VROOWH# LP6FK�OHUH[SHULPHQW# HUIROJHQ1# (LQH# HQWVSUHFKHQGH$QOHLWXQJ#LVW#LP#$+#61#46#HQWKDOWHQ1(LQH#$XVZHUWXQJ# GHV# 6FK�OHUH[SHULPHQWV# I�KUW# ]XGHP#(UJHEQLV#)4#ü#O4 ≈ )5#ü#O51#

'LH#*ROGHQH#5HJHO#GHU#0HFKDQLN#NDQQ#PDQ#DXIVHKU# YHUVFKLHGHQHP# 1LYHDX# IRUPXOLHUHQ/# ZREHL# ]XEHDFKWHQ#LVW/#GDVV#GLH#$QZHQGXQJVEUHLWH#GHU#HLQ]HO0QHQ# )RUPXOLHUXQJHQ# XQWHUVFKLHGOLFK# LVW1# :HOFKH9DULDQWH#GHU#/HKUHU#ZlKOW/#VROOWH#YRP#/HLVWXQJVYHU0P|JHQ# GHU# EHWUHIIHQGHQ# .ODVVH# DEKlQJLJ# JHPDFKWZHUGHQ1#0|JOLFKH#)RUPXOLHUXQJHQ#VLQG=

7DIHOELOG

² :DV#PDQ#DQ#.UDIW#VSDUW/#PXVV#PDQ#DQ#:HJ#]XVHW0]HQ1

² 'LH#HUIRUGHUOLFKH#.UDIW#LVW#XPVR#NOHLQHU/# MH#JU|�HUGHU#]XU�FNJHOHJWH#:HJ#LVW1

² 'LH#HUIRUGHUOLFKH#.UDIW#LVW#XPJHNHKUW#SURSRUWLRQDOGHP#:HJ#+)a42V,1

² 'LH# ZLUNHQGHQ# .UlIWH# YHUKDOWHQ# VLFK# XPJHNHKUWSURSRUWLRQDO#GHQ#]XU�FNJHOHJWHQ#:HJHQ#+)4#2)5# #V5#2V4,1

² 'LH# 3URGXNWH# DXV# MHZHLOV# ZLUNHQGHU# .UDIW# XQG]XU�FNJHOHJWHP#:HJ#VLQG#JOHLFK#JUR�#+)4#ü#V4# #)5#ü#V5,1

,P# ,QWHUHVVH# HLQHV# OHEHQVQDKHQ# 3K\VLNXQWHUULFKWVLVW#GHQ#6FK�OHUQ#GHXWOLFK# ]X#PDFKHQ/#GDVV#GLH#*RO0GHQH#5HJHO# LQ#GHU#3UD[LV#QXU# LQ#PHKU#RGHU#PLQGHUJXWHU#1lKHUXQJ# JLOW/# GD# DOOH#%HZHJXQJHQ#PLW#5HL0EXQJ#YHUEXQGHQ#VLQG1#+LHU#ZLUG#GHXWOLFK=#1XU#GXUFK,GHDOLVLHUXQJHQ# +KLHU= 9HUQDFKOlVVLJXQJ# GHU# 5HL0EXQJ,# ODVVHQ# VLFK# LQ# GHU# 3K\VLN#*HVHW]H# LQ# UHODWLYHLQIDFKHU#)RUP#IRUPXOLHUHQ1#'HU#/HKUHU#VROOWH#EHDFK0WHQ/# GDVV# GLHV# I�U# 6FK�OHU# GLHVHU# $OWHUVVWXIH# QXUVFKZHU#QDFK]XYROO]LHKHQ# LVW#XQG# OHLFKW# ]X#GHU#0HL0QXQJ#I�KUW/#GDVV#3K\VLN#ZHQLJ#PLW#GHQ#WDWVlFKOLFKHQ*HJHEHQKHLWHQ#]X#WXQ#KDW1#'HP#VROOWH#EHZXVVW#HQWJH0JHQJHZLUNW#ZHUGHQ1

$OV#=XVDPPHQIDVVXQJ#NDQQ#GDV#EHLOLHJHQGH#$UEHLWV0EODWW#GLHQHQ1

+HEHO

(LQVHLWLJHU#+HEHO =ZHLVHLWLJHU#+HEHO

%HLVSLHOH= %HLVSLHOH=7�UNOLQNH :LSSH%UHFKVWDQJH :DDJH1XVVNQDFNHU 5RKU]DQJH

Page 24: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

39

#$UEHLWVEODWW

.UDIWXPIRUPHQGH#(LQULFKWXQJHQ#4

41 (UJlQ]H#GLH#hEHUVLFKW#]X#5ROOHQ$

IHVWH#5ROOH ORVH#5ROOH )ODVFKHQ]XJ

51 6NL]]LHUH#HLQHQ#]ZHLVHLWLJHQ#+HEHO$#1HQQH#]X#MHGHU#+HEHODUW#]ZHL#%HLVSLHOH$

HLQVHLWLJHU#+HEHO ]ZHLVHLWLJHU#+HEHO

61 :LH#ODXWHW#GDV#+HEHOJHVHW]"

71 (UJlQ]H#LQ#GHQ#6NL]]HQ#GLH#.UDIWSIHLOH$#%HDFKWH/#GDVV#GLH#/lQJH#GHU#3IHLOH#HLQ0D�#I�U#GHQ#%HWUDJ#GHU#.UDIW#LVW$D, E, F,

81#:LH#ODXWHW#GLH#*ROGHQH#5HJHO#GHU#0HFKDQLN$

Page 25: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Kraftumformende Einrichtungen

40

#$UEHLWVEODWW

.UDIWXPIRUPHQGH#(LQULFKWXQJHQ#5

41 5ROOHQ# VLQG# YHUVFKLHGHQ# DQJHRUGQHW1# 'LH# *HZLFKWVNUDIW# GHV# DQJHKlQJWHQ# .|USHUVEHWUlJW#MHZHLOV#433#11#:HOFKH#=XJNUDIW#)4#LVW#PLQGHVWHQV#HUIRUGHUOLFK/#XP#GLH#/DVW#]XKDOWHQ"

51 8QWHU#ZHOFKHU#%HGLQJXQJ#LVW#HLQ#+HEHO#LP#*OHLFKJHZLFKW"

61 'LH#+HEHO#VROOHQ#VLFK#LP#*OHLFKJHZLFKW#EHILQGHQ1#1HQQH#P|JOLFKH#:HUWH#I�U#)4#XQG#)5#$'LH#+HEHO#KDEHQ#HLQH#FP07HLOXQJ1

71 'LH#+HEHO#EHILQGHQ#VLFK#LP#*OHLFKJHZLFKW1#0DUNLHUH#MHZHLOV#GLH#'UHKDFKVH$#%HJU�QGH$'LH#+HEHO#KDEHQ#HLQH#FP07HLOXQJ1

Page 26: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

41

71 41 8 0HFKDQLVFKH#$UEHLW#XQG#/HLVWXQJ

:LH# YLHOH# DQGHUH# %HJULIIH# VLQG# GHQ# 6FK�OHUQ# GLH%HJULIIH#$UEHLW# XQG# /HLVWXQJ# DXV# GHQ# XQWHUVFKLHG0OLFKVWHQ#=XVDPPHQKlQJHQ#EHNDQQW1#'HVKDOE#GUlQJWHV#VLFK#JHUDGH]X#DXI/#]XQlFKVW#HLQPDO#PLW# LKQHQ#]XVDPPHOQ/#LQ#ZHOFKHQ#=XVDPPHQKlQJHQ#XQG#%HGHX0WXQJHQ#GHU#%HJULII#$UEHLW#YHUZHQGHW#ZLUG/#HKH#PDQ]XP#SK\VLNDOLVFKHQ#%HJULII#GHU#PHFKDQLVFKHQ#$UEHLW�EHUJHKW1

'DEHL#VROOWH#PDQ#YHUPHLGHQ/#GLH#8PJDQJVVSUDFKH#DOVXQJHQDX#RGHU#XQNODU#RGHU#QLFKW#SUl]LVH#]X#FKDUDNWH0ULVLHUHQ1# (V# JHKW# QLFKW# GDUXP/# GDVV# GLH# 8PJDQJV0VSUDFKH# XQJHQDX# XQG# GLH# )DFKVSUDFKH# EHVRQGHUVH[DNW# LVW# +ZDV# �EULJHQV# EHLGHV# QLFKW# VWLPPW,/# VRQ0GHUQ#GDUXP/#]X#NOlUHQ/#ZDV#PDQ#LQ#GHU#3K\VLN#XQWHUPHFKDQLVFKHU#$UEHLW#YHUVWHKW1#(V#JLOW#DOVR/#8PIDQJXQG# ,QKDOW# GHV# SK\VLNDOLVFKHQ# %HJULIIV# GHXWOLFK# ]XPDFKHQ1

8P#GHQ#%HJULII#PHFKDQLVFKH#$UEHLW#]X#NOlUHQ/#ELHWHQVLFK# HLQIDFKH#([SHULPHQWH#DQ/#GLH# MHZHLOV#NRPPHQ0WLHUW#ZHUGHQ1#'D]X#HLJQHQ#VLFK#]1 %1#IROJHQGH#([SHUL0PHQWH=

41 (LQ#.|USHU#+:lJHVW�FN/#%XFK,#ZLUG#JHKREHQ1.RPPHQWDU=# $XI# GHQ# .|USHU# ZLUNW# HLQH# .UDIW1'HU#.|USHU#ZLUG#GDGXUFK#EHZHJW1#(V#ZLUG#PHFKD0QLVFKH#$UEHLW#YHUULFKWHW1

51 (LQ#/LQHDO/#HLQH#%ODWWIHGHU#RGHU#HLQ#+RO]VWDE#ZLUGJHERJHQ1

61 (LQ#.|USHU#ZLUG#LQ#GHU#+DQG#JHKDOWHQ1

71 (LQ#.|USHU#+%DOO/#6WHLQ,#IlOOW#QDFK#XQWHQ1

81 (LQ#+RO]NORW]#ZLUG#PLW#NRQVWDQWHU#*HVFKZLQGLJ0NHLW#�EHU#GHQ#([SHULPHQWLHUWLVFK#JH]RJHQ1

91 (LQ#([SHULPHQWLHUZDJHQ#ZLUG#EHVFKOHXQLJW1

:1 (LQ#6W�FN#.QHWH#ZLUG#YHUIRUPW1

$Q# HLQIDFKHQ# %HLVSLHOHQ# +]1 %1# =LHKHQ# YHUVFKLHGHQVFKZHUHU#.|USHU#�EHU# HLQH#EHVWLPPWH#6WUHFNH/#=LH0KHQ# HLQHV# .|USHUV# HLQH# NXU]H# XQG# HLQH# OlQJHUH6WUHFNH/# 'HKQHQ# HLQHV# ([SDQGHUV#PLW# HLQHU# )HGHUE]Z1#PLW# ]ZHL# )HGHUQ# XP# HLQH# EHVWLPPWH# 6WUHFNH/XQWHUVFKLHGOLFK#ZHLWHV#$XV]LHKHQ#HLQHU#)HGHU,#NDQQGHQ# 6FK�OHUQ# SODXVLEHO# JHPDFKW# ZHUGHQ/# GDVV# GLHPHFKDQLVFKH#$UEHLW#YRQ#.UDIW#XQG#:HJ#DEKlQJW/#HVDOVR#VLQQYROO#LVW/#GLH#PHFKDQLVFKH#$UEHLW#DOV#3URGXNWDXV#.UDIW#XQG#:HJ#]X#GHILQLHUHQ1

$XIJDEHQ#]XU#)HVWLJXQJ#VLQG#LP#$+#61#48 ²49#XQG#LP

/%#61 :6#HQWKDOWHQ1#'LH#YHUVFKLHGHQHQ#$UWHQ#PHFKD0QLVFKHU# $UEHLW# N|QQHQ# DQKDQG# HLQIDFKHU# ([SHUL0PHQWH# XQWHU# (LQEH]LHKXQJ# GHU# hEHUVLFKW# LP# /%61 97#DQ#GLH#6FK�OHU#KHUDQJHWUDJHQ#ZHUGHQ1#(V#JHKWGDEHL#XP#HLQHQ#HUVWHQ#hEHUEOLFN1

%HL#GHU#(LQWHLOXQJ#LQ#YHUVFKLHGHQH#$UWHQ#YRQ#$UEHLWVROOWH#YRP#/HKUHU#EHDFKWHW#ZHUGHQ/#GDVV#EHL# UHDOHQ9RUJlQJHQ# PHLVW# PHKUHUH# $UWHQ# YRQ# $UEHLW# HLQH5ROOH# VSLHOHQ1# 6R# ZLUG# HWZD# EHLP# $QIDKUHQ# HLQHV$XWRV# QLFKW# QXU# %HVFKOHXQLJXQJVDUEHLW# YHUULFKWHW/VRQGHUQ# DXFK#5HLEXQJVDUEHLW1#'LHV# OHLWHW# XQPLWWHO0EDU#�EHU#]X#GHU#8QWHUVFKHLGXQJ#]ZLVFKHQ#DXI]XZHQ0GHQGHU#XQG#QXW]EULQJHQGHU#$UEHLW1#=X# HPSIHKOHQ# LVW# GLH# (UOlXWHUXQJ# GLHVHU# %HJULIIHDQKDQG#HLQHV#NRQNUHWHQ#%HLVSLHOV/#VR#ZLH#HV#EHLVSLHO0KDIW#LP#/%#61 9<#GDUJHVWHOOW#LVW10LW# GLHVHU# 8QWHUVFKHLGXQJ# ZHUGHQ# H[SHULPHQWHOOH(UJHEQLVVH# EHVVHU# YHUVWlQGOLFK1# =XJOHLFK# ZLUG# GHU%HJULII# GHV# :LUNXQJVJUDGHV# LQKDOWOLFK# YRUEHUHLWHW/RKQH#GDVV#GHU#7HUPLQXV#EHUHLWV#HLQJHI�KUW#ZLUG1#)�UGHQ#8QWHUULFKW#VROOWHQ#IROJHQGH#$VSHNWH#EHU�FNVLFK0WLJW#ZHUGHQ=

² (LQLJH# *U|�HQYRUVWHOOXQJHQ# �EHU# PHFKDQLVFKH$UEHLWHQ# LQ# 1DWXU# XQG# 7HFKQLN# YHUPLWWHOW# GLH7DEHOOH#LP#/%#61#961#)�U#GLH#6FK�OHU#HLQSUlJVDPHULVW# HV/#ZHQQ# VLH#$UEHLWHQ# HUPLWWHOQ/#GLH# LQ# LKUHP(UIDKUXQJVEHUHLFK#HLQH#5ROOH#VSLHOHQ/#]1 %1=� :HOFKH#$UEHLW#YHUULFKWH# LFK/#ZHQQ# LFK# 43#7UHS0SHQVWXIHQ#KRFKVWHLJH"

� :HOFKH# $UEHLW# YHUULFKWH# LFK/# ZHQQ# LFK# HLQHQ6WHLQ#LQ#HLQH#EHVWLPPWH#+|KH#KHEH"

� :HOFKH# $UEHLW# YHUULFKWH# LFK/# ZHQQ# LFK# HLQHQ+|KHQXQWHUVFKLHG#YRQ#433#P#]XU�FNOHJH"#

² (LQEH]RJHQ#ZHUGHQ#VROOWHQ#LQ#GLH#'LVNXVVLRQ#DXFK)lOOH/# EHL# GHQHQ# GLH# 6FK�OHU# HUIDKUXQJVJHPl�6FKZLHULJNHLWHQ#KDEHQ#]X#HUNHQQHQ/#RE#$UEHLW#YHU0ULFKWHW# ZLUG# RGHU# QLFKW1# 'D]X# JHK|UW# ]1 %1# GLHJOHLFKI|UPLJH# )DKUW# HLQHV# $XWRV# RGHU# HLQHV# 5DG0IDKUHUV#DXI#HEHQHU#6WUHFNH/#ZR#GLH#5HLEXQJVDUEHLWJHQDXVR#JUR�#LVW#ZLH#GLH#YRP#0RWRU#E]Z1#YRP#)DK0UHU#YHUULFKWHWH#$UEHLW1

² )�U#6FK�OHU#LVW#HV#LPPHU#ZLHGHU#VFKZHU#YHUVWlQG0OLFK/# GDVV# HV# ]ZDU# DQVWUHQJHQG# LVW/# HLQH# VFKZHUH7DVFKH# LQ# GHU# +DQG# ]X# KDOWHQ/ GLHV# DEHU# NHLQH$UEHLW#LP#SK\VLNDOLVFKHQ#6LQQH#VHLQ#VROO1+LHU# LVW#GDUDXI# DXIPHUNVDP# ]X#PDFKHQ/#GDVV#GLH3K\VLN# QXU# HLQHQ# $VSHNW# EHWUDFKWHW1#'D# YRQ# GHU7DVFKH# NHLQ# :HJ# ]XU�FNJHOHJW# ZLUG/# LVW# ZHJHQ: )#ü#V#GLH#$UEHLW#QXOO11LFKW#EHWUDFKWHW#ZHUGHQ#LQ#GHU#3K\VLN#GLH#PLNURV0NRSLVFKHQ# 9RUJlQJH# LQ# GHQ# 0XVNHOQ1# ,Q# LKQHQHUIROJHQ#VWlQGLJ#$QVSDQQXQJHQ#XQG#(QWVSDQQXQ0JHQ/# YHUEXQGHQ# PLW# PLNURVNRSLVFKHQ# %HZHJXQ0

Page 27: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

42

JHQ1# 'D]X# LVW# (QHUJLH# HUIRUGHUOLFK1# 'LH# $Q0VWUHQJXQJ#EHLP#+DOWHQ#HLQHU#7DVFKH#LVW#QLFKW#QXUHLQH#VXEMHNWLYH#(PSILQGXQJ1#:LU#YHUULFKWHQ#GDEHLSK\VLRORJLVFKH#$UEHLW1#'LHVH#ZLUG# DEHU# LQ# GHU3K\VLN# QLFKW# EHWUDFKWHW1# $XI# GLHVH# $VSHNWKDIWLJ0NHLW# GHU#3K\VLN# VROOWH#PDQ#6FK�OHU# VHKU# GHXWOLFKDXIPHUNVDP#PDFKHQ1

² 1LFKW#VHOWHQ#ZLUG#GDV#*HKHQ#DXI#HEHQHU#6WUHFNH#DOV%HLVSLHO#GDI�U#JHQRPPHQ/#GDVV#WURW]#=XU�FNOHJHQHLQHV#:HJHV#NHLQH#$UEHLW#YHUULFKWHW#ZLUG/#GD#.UDIWXQG#:HJ#VHQNUHFKW#]XHLQDQGHU#VLQG1(LQH# HWZDV# JHQDXHUH# $QDO\VH# GHV# %HZHJXQJVDE0ODXIHV#EHLP#*HKHQ#]HLJW#DOOHUGLQJV/#GDV#ZLU#GDEHLXQVHUHQ#.|USHU# VWlQGLJ# KHEHQ# XQG# VHQNHQ/# DOVREHLP#*HKHQ#+XEDUEHLW#YHUULFKWHW#ZLUG1#6HW]W#PDQGHQ#(QHUJLHDXIZDQG#EHLP#*HKHQ#PLW#433(#DQ/#VRZHUGHQ#DOOHLQ# I�U#GLH#+XEDUEHLW#93(#ELV#:3(#GHU(QHUJLH#EHQ|WLJW1#%HLP#*HKHQ# LQ#GHU#(EHQH#ZLUGDOVR# LQ# HUKHEOLFKHP#8PIDQJH#+XEDUEHLW# YHUULFK0WHW1

² (LQH#'LIIHUHQ]LHUXQJ#GDKLQJHKHQG/#RE#YRQ# HLQHP.|USHU# RGHU# DQ# HLQHP# .|USHU# $UEHLW# YHUULFKWHWZLUG/#LVW#I�U#GHQ#$QIDQJVXQWHUULFKW#QLFKW#HUIRUGHU0OLFK1#(V# VROOWH# KLHU# YLHOPHKU# GLH# NRQNUHWH# $UEHLWEHQDQQW#ZHUGHQ/#XP#GLH#HV#MHZHLOV#JHKW1

'LH# (LQI�KUXQJ# GHU# PHFKDQLVFKHQ# /HLVWXQJ# DOV$UEHLWVJHVFKZLQGLJNHLW#EHUHLWHW#L1#$OOJ1#NHLQH#6FKZLH0ULJNHLWHQ/#ZHQQ#PDQ#YRQ#NRQNUHWHQ#%HLVSLHOHQ#DXV0JHKW1#'D]X#HLJHQHQ#VLFK#X1 D1#IROJHQGH#%HLVSLHOH=² 0HQVFKHQ#JOHLFKHU#0DVVH#VWHLJHQ#LQ#XQWHUVFKLHGOL0FKHQ#=HLWHQ#HLQH#7UHSSH#KRFK1

² 0HQVFKHQ#XQWHUVFKLHGOLFKHU#0DVVH# VWHLJHQ# LQ#GHUJOHLFKHQ#=HLW#HLQH#7UHSSH#KRFK1

² .|USHU#XQWHUVFKLHGOLFKHU#*HZLFKWVNUDIW#ZHUGHQ#LQJOHLFKHU#=HLW#HLQH#EHVWLPPWH#6WUHFNH#JHKREHQ#E]Z1HLQ#.|USHU#ZLUG# LQ#XQWHUVFKLHGOLFKHQ#=HLWHQ#GLHVH6WUHFNH#JHKREHQ1

:LFKWLJ#LVW/#GDVV#DQKDQG#GHU#%HLVSLHOH#GHQ#6FK�OHUQGLH#=XVDPPHQKlQJH#GHXWOLFK#ZHUGHQ=#'LH#/HLVWXQJLVW#XPVR#JU|�HU/² MH#N�U]HU#GLH#=HLW#LVW/#LQ#GHU#HLQH#EHVWLPPWH#$UEHLWYHUULFKWHW#ZLUG#RGHU

² MH#JU|�HU#GLH#YHUULFKWHWH#$UEHLW# LQ#HLQHU#EHVWLPP0WHQ#=HLW#LVW1

'LH#=XVDPPHQKlQJH#N|QQHQ#LQ#HLQHP#7DIHOELOG#YHU0GHXWOLFKW#ZHUGHQ1)�U#GLH#)HVWLJXQJ#ELHWHW#GDV#/%#61# :7 ²:8#XQG#GDV$+#61 4:#HLQ#$XIJDEHQDQJHERW1

'DU�EHU#KLQDXV#ELHWHQ# VLFK# IROJHQGH#6FKZHUSXQNWHDQ/# GLH# I�U# 6FK�OHU# HUIDKUXQJVJHPl�# LQWHUHVVDQWVLQG/#DXV#GHQHQ#GHU#/HKUHU/#HYHQWXHOO#]XVDPPHQ#PLWVHLQHQ#6FK�OHUQ/#DEHU#DXVZlKOHQ#VROOWH=

41'DPLW#GLH#6FK�OHU#*U|�HQYRUVWHOOXQJHQ#YRQ#/HLV0WXQJHQ# HUKDOWHQ/# N|QQWHQ# YRQ# GHQ# 6FK�OHUQ# GLH/HLVWXQJHQ# YRQ# )DKU]HXJHQ# HUNXQGHW# ZHUGHQ1'DEHL# VWR�HQ#GLH#6FK�OHU#]1 %1#EHL#$XWRV#DXI#/HL0VWXQJVDQJDEHQ#LQ#361#,P#,QWHUHVVH#GHU#/HEHQVYHU0EXQGHQKHLW# GHV#8QWHUULFKWV# VROOWH#PDQ# DXI# GLHVH(LQKHLW#PLW#HLQJHKHQ1=X# EHDFKWHQ# LVW# EHL# GHQ# /HLVWXQJVDQJDEHQ# YRQ)DKU]HXJHQ/# GDVV# �EOLFKHUZHLVH# GLH# 0D[LPDOOHL0VWXQJHQ#DQJHJHEHQ#ZHUGHQ/#GLH#ZHLW#�EHU#GHQ#/HL0VWXQJHQ#OLHJHQ/#GLH#EHL#QRUPDOHU#)DKUW#HUIRUGHUOLFKVLQG1

51 ,QWHUHVVDQW# LVW# I�U# YLHOH# 6FK�OHU# GLH# )UDJH/# ZLHJUR�#GLH# HLJHQH#/HLVWXQJ# LVW#XQG#GDPLW#QDW�UOLFKDXFK/#ZLH#PDQ#VLH#EHVWLPPHQ#NDQQ1#=X#XQWHUVFKHL0GHQ#LVW#GDEHL#VWHWV#]ZLVFKHQ#/HLVWXQJHQ#�EHU#HLQHOlQJHUH# =HLW# KLQZHJ# +KLHU# VLQG# 433:# ELV# 533:P|JOLFK,#XQG#/HLVWXQJHQ/#GLH#QXU#LQ#HLQHP#NXU]HQ=HLWUDXP# HUEUDFKW# ZHUGHQ# N|QQHQ# +]1 %1# EHLP+RFKVSUXQJ#RGHU#EHLP#*HZLFKWKHEHQ>#GLH#+|FKVW0OHLVWXQJHQ#OLHJHQ#EHL#HWZD#4/8#N:,1#)�U#VROFKH#/HLV0WXQJVEHVWLPPXQJHQ/# GLH# PDQ# DXFK# DOV# :HWW0EHZHUE#]ZLVFKHQ#GHQ#6FK�OHU#JHVWDOWHQ#NDQQ/#HLJ0QHW# VLFK# EHVRQGHUV# GDV# 7UHSSHQVWHLJHQ# RGHU# GDV.OHWWHUQ#DQ#HLQHU#.OHWWHUVWDQJH1#*HZLFKWVNUDIW#GHU3HUVRQ#XQG#+|KH#GHU#7UHSSHQVWXIHQ#E]Z1#+XEK|KHEHLP# .OHWWHUQ# ODVVHQ# VLFK# OHLFKW# EHVWLPPHQ/# GLH=HLW#NDQQ#PLW#HLQHU#6WRSSXKU#JHPHVVHQ#ZHUGHQ1'HU#/HKUHU#VROOWH#EHDFKWHQ/#GDVV#]X#GLHVHU#/HLVWXQJEHL#MHGHP#0HQVFKHQ#QRFK#GHU#*UXQGXPVDW]#KLQ0]XNRPPW/#DOVR#GLH#(QHUJLH#SUR#=HLW/#GLH#GHU#0HQVFKI�U# GLH# $XIUHFKWHUKDOWXQJ# VHLQHU# /HEHQVIXQNWLR0QHQ#EHQ|WLJW1#'HU#*UXQGXPVDW]#EHWUlJW#LP#'XUFK0VFKQLWW# ;3#:1# $QJDEHQ# ]XU# (QHUJLHXPVHW]XQJ# MH=HLWHLQKHLW#I�U#YHUVFKLHGHQH#PHQVFKOLFKH#7lWLJNHL0WHQ# ILQGHW# GHU#/HKUHU# LP#3$(7(&#7DIHOZHUN# I�UGLH#6HN1#,#XQG#,,/#7HLO#%LRORJLH1)�U#HLQH#]XVDPPHQIDVVHQGH#)HVWLJXQJ#NDQQ#DXFKGDV#EHLOLHJHQGH#$UEHLWVEODWW#JHQXW]W#ZHUGHQ1

)DKU]HXJ /HLVWXQJ

+0HQVFK/#'XUFKVFKQLWWVOHLVWXQJ, 433#:

3.:#)LDW#&LQTXHFHQWR 5<#N:#2#73#36

3.:#*ROI#,,#41;#RGHU#2SHO#$VWUD#419L

88#N:#2#:8#36

3.:#0HUFHGHV#(#533 443#N:#2#483#36

3.:#3RUVFKH#<77#7XUER 4;7#N:#2#583#36

PLWWOHUHU#/.: 583#N:

$QWULHEVHLQKHLW#GHV#,&( 8#0:

3DVVDJLHUIOXJ]HXJ 93#0:

JUR�H#5DNHWH 83 333#0:

Page 28: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

43

'HU# =XVDPPHQKDQJ# ]ZLVFKHQ# $UEHLW# XQG# (QHUJLHVROOWH#DQ#HLQIDFKHQ#%HLVSLHOHQ#YHUGHXWOLFKW#ZHUGHQ=² :HQQ#PDQ# HLQHQ#6WHLQ#KRFKKHEW/#YHUJU|�HUW# VLFKVHLQH# SRWHQWLHOOH# (QHUJLH1# :HQQ# PDQ# LKQ# IDOOHQOlVVW/#LVW#HU#LQ#GHU#/DJH/#.|USHU#]X#YHUIRUPHQ/#DOVR$UEHLW#]X#YHUULFKWHQ1

² (LQ# IDKUHQGHV# $XWR# EHVLW]W# NLQHWLVFKH# (QHUJLH1:HQQ#HV# ]1%1#JHJHQ# HLQHQ#%DXP# IlKUW/# VR#YHUULQ0JHUW#VLFK#VHLQH#NLQHWLVFKH#(QHUJLH1#(V#ZLUG#Å9HUIRU0PXQJVDUEHLW´#YHUULFKWHW1

:LFKWLJ# LVW/#GDVV#GLH#6FK�OHU# IROJHQGH# ]ZHL#$VSHNWHHUIDVVHQ=² 9HUULFKWHQ#YRQ#$UEHLW#DQ#HLQHP#.|USHU# I�KUW#]XUbQGHUXQJ#VHLQHU#(QHUJLH1

² bQGHUW#VLFK#GLH#(QHUJLH#HLQHV#.|USHUV/#VR#NDQQ#GDVPLW#GHP#9HUULFKWHQ#YRQ#$UEHLW#YHUEXQGHQ#VHLQ1

7DIHOELOG

'LH#=XVDPPHQKlQJH# ]ZLVFKHQ#PHFKDQLVFKHU#(QHU0JLH#XQG#$UEHLW#VLQG#LP#7%#]XVDPPHQIDVVHQG#GDUJH0VWHOOW1

%HL# GHU# +LQI�KUXQJ# ]XP# (QHUJLHHUKDOWXQJVVDW]HUVFKHLQW# HV# VLQQYROO/# LP# +LQEOLFN# DXI# SUDNWLVFKH$QZHQGXQJHQ# GHQ# 6FK�OHUQ# HLQHQ# hEHUEOLFN# �EHUYHUVFKLHGHQH# (QHUJLHIRUPHQ# XQG# (QHUJLHWUlJHU# ]XJHEHQ1# 'D]X# NDQQ# GLH# EHLOLHJHQGH# .RSLHUYRUODJHJHQXW]W# ZHUGHQ1# 'DU�EHU# KLQDXV# ZLUG# HPSIRKOHQ/GHQ#DOOJHPHLQHQ#(QHUJLHHUKDOWXQJVVDW]#GHXWOLFK#KHU0DXV]XKHEHQ/# GD# GHU# (QHUJLHHUKDOWXQJVVDW]# GHU0HFKDQLN# QXU# HLQH# JHULQJH# $QZHQGXQJVEUHLWH# KDWXQG#VFKRQ#EHL#YLHOHQ#$QZHQGXQJHQ#DXV#GHP#(UIDK0UXQJVEHUHLFK#GHU#6FK�OHU#QLFKW#DQZHQGEDU#LVW1

'LH#PHFKDQLVFKH#$UEHLW

0HFKDQLVFKH#$UEHLW#ZLUG#YHUULFKWHW/#ZHQQ#HLQ#.|USHU#GXUFK#HLQH#.UDIW#EHZHJW#RGHU#YHUIRUPW#ZLUG1

:HQQ#GLH#.UDIW#)#NRQVWDQW#LVW#XQG#LQ#5LFKWXQJ#GHV#:HJHV#V#ZLUNW/#GDQQ#JLOW=

PHFKDQLVFKH#$UEHLW# #ZLUNHQGH#.UDIW#ü#]XU�FNJHOHJWHU#:HJ

:# #)#ü#V

(LQKHLWHQ= 4#1HZWRQPHWHU#+4#1P,4#1P# #4#-

4#-RXOH#+4#-,

Page 29: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

44

7DIHOELOG

7DIHOELOG

'LH#PHFKDQLVFKH#/HLVWXQJ

'LH#PHFKDQLVFKH#/HLVWXQJ#JLEW#DQ/#ZLH#YLHO#PHFKDQLVFKH#$UEHLW#LQ#MHGHU#6HNXQGH#YHU0ULFKWHW#ZLUG1

YHUULFKWHWH#PHFKDQLVFKH#$UEHLW # :/HLVWXQJ# #²²²²²²²²²²²²²²²²²²²²²²²²²²²² # 3 ²²

=HLW # W

(LQKHLWHQ=

4#36 #:69#:

*OHLFKH#$UEHLW#LQ#YHUVFKLHGHQHU#=HLW 9HUVFKLHGHQH#$UEHLW#LQ#JOHLFKHU#=HLW

:4# # :5# :4# ?# :5#

W4# ?# W5# W4# W5#34# !# 35 34# ?# 35#

4-V000 4 1P

V0000000000 4#:#+4#:DWW,

0HFKDQLVFKH#$UEHLW#XQG#PHFKDQLVFKH#(QHUJLH

)�U#GHQ#=XVDPPHQKDQJ#]ZLVFKHQ#$UEHLW#XQG#(QHUJLH#JLOW=

+XEDUEHLW# RGHU# 6SDQQDUEHLW# I�KUW]X#HLQHU#bQGHUXQJ#GHU#SRWHQWLHOOHQ(QHUJLH1

%HVFKOHXQLJXQJVDUEHLW# I�KUW# ]X# HLQHUbQGHUXQJ#GHU#NLQHWLVFKHQ#(QHUJLH1

:# #∆ ∆ ∆ ∆ (

Page 30: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

45

#$UEHLWVEODWW

41 (UJlQ]H#GLH#IROJHQGH#hEHUVLFKW#]XU#PHFKDQLVFKHQ#$UEHLW#XQG#/HLVWXQJ$

51 *LE#DQ/#RE#LQ#GHQ#VNL]]LHUWHQ#)lOOHQ#PHFKDQLVFKH#$UEHLW#YHUULFKWHW#ZLUG$%HJU�QGH#GHLQH#$XVVDJHQ$

D, E, F,

61 %HVWLPPH#MHZHLOV/#ZHOFKH#PHFKDQLVFKH#$UEHLW#YHUULFKWHW#ZLUG$D, E, F,

71 %HVWLPPH#MHZHLOV#GLH#PHFKDQLVFKH#$UEHLW#XQG#GLH#PHFKDQLVFKH#/HLVWXQJ$D, E, F,

3K\VLNDOLVFKH#*U|�H *OHLFKXQJ#]XU#%HUHFKQXQJ (LQKHLWHQPHFKDQLVFKH#$UEHLW

1 Js-- =

1PS =

Page 31: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

46

#$UEHLWVEODWW

$UEHLW#XQG#(QHUJLH

41 (LQH#%HWRQSODWWH#ZLUG#PLW#+LOIH#HLQHU# ORVHQ5ROOH# YRP#%RGHQ# DXV# LQ# 6/8#P#+|KH# JHKR0EHQ1D, 0LW#ZHOFKHU#.UDIW#)#PXVV#PLQGHVWHQV#DP6HLO#JH]RJHQ#ZHUGHQ"

E, :LH#JUR�# LVW#GLH#YHUULFKWHWH#PHFKDQLVFKH$UEHLW"

F, (UOlXWHUH#GHQ#=XVDPPHQKDQJ#]ZLVFKHQ#GHU#YHUULFKWHWHQ#$UEHLW#XQG#GHU#bQGHUXQJGHU#PHFKDQLVFKHQ#(QHUJLH$

51 :DV#YHUVWHKW#PDQ#LQ#GHU#3K\VLN#XQWHU#$UEHLW/#ZDV#XQWHU#(QHUJLH"$UEHLW#: (QHUJLH#(

61 $Q#HLQHU#)HGHU# LVW#HLQ#.|USHU#EHIHVWLJW1#'HU#.|USHUZLUG#DQJHKREHQ#XQG#GDQQ#ORVJHODVVHQ1D, %HVFKUHLEH#GHQ#9RUJDQJ#PLW#GHQ#%HJULIIHQ#$UEHLW/(QHUJLH/#SRWHQWLHOOH#(QHUJLH/#NLQHWLVFKH#(QHUJLH$

E, :DUXP#K|UW#GDV#+LQ0#XQG#+HUVFKZLQJHQ#GHV#.|USHUV#QDFK#HLQLJHU#=HLW#DXI"

Page 32: 7 (PSIHKOXQJHQ XQG 0DWHULD0 ]XU - Duden  · PDF filebewegung von körpern 16 7 (psihkoxqjhq#xqg#0dwhuld0 olhq#]xu#8qwhuulfkwvjhvwdowxqj 714 0hfkdqln

Mechanische Arbeit und Leistung

47

#.RSLHUYRUODJH

(QHUJLH/#(QHUJLHIRUPHQ/#(QHUJLHWUlJHU

(QHUJLH#LVW#GLH#)lKLJNHLW#HLQHV#.|USHUV/#PHFKDQLVFKH#$UEHLW#]X#YHUULFKWHQ#RGHU:lUPH#DE]XJHEHQ#RGHU#/LFKW#DXV]XVHQGHQ1

(QHUJLHIRUP %HLVSLHOH (QHUJLHWUlJHU

SRWHQWLHOOH#(QHUJLH(SRW

DQJHVWDXWHV#:DVVHUJHKREHQH#.|USHU

NLQHWLVFKH#(QHUJLH(NLQ

IDKUHQGHV#$XWRVWU|PHQGHV#:DVVHUVWU|PHQGH#/XIW

WKHUPLVFKH#(QHUJLH(WKHUP

KHL�HU#2IHQKHL�HV#:DVVHU)ODPPH#HLQHU#.HU]H

FKHPLVFKH#(QHUJLH(FKHP

6WHLQNRKOH/#%UDXQNRKOH#(UGJDV/#3URSDQ%HQ]LQ/#'LHVHONUDIWVWRII#+HL]|O1DKUXQJVPLWWHO

HOHNWULVFKH#(QHUJLH(HO

HOHNWULVFKHU#6WURP

.HUQHQHUJLH(NHUQ

:DVVHUVWRII/#8UDQ/#3OXWR0QLXP