1348660483 Studyguide 2 CHI Gray

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6

A.

#p #q #p + #q

d s (m)

t = 2 s = 4ms1

vavg = 4/2= 2ms1 +

= dtot

ttot v

vavg = stotttot ms1


a

a = v ut ms2

B

s + v + a +

s + v + a +

s =(u+ v2

)t

s = vavgt = (u+ v2

)t v = u+at s = ut + 12 at 2 v2u2 = 2as


6 v = > 0

v = < 0

a = > 0

a = < 0

(a =g =9.81ms2)


B.

CE-- Q

V

V CE-- Q

V


6C. i 1

2

3

1

2

3

4

(a) t = 0 30 s

(4)(b) t = 0 30 s (i) (ii) (3)(a) . t = 10 s

. s . st vt

AAv1 =

80

100 = 8ms1v2 =

40803010 =6ms1

(2A)

t = 0 10 s 8ms1 (1A) t = 10 30 s 6ms1 (1A)(b) (i) =40m (1A)

B (ii) = = (280)+4030 6.67ms1 (1M+1A)

t = 30 s st t = 30 s


30 ms1 80 m v t

(a) (i) (1)(ii) (1)(b) (1)(c) (2)

(a) t = 0 0.2 s t = 0.2 5 s

= t = 0 0.2 s = t = 0.2 5 s(i) = (30)(0.2)= 6m (1A)(ii) = (30)(50.2)

2= 72m (1A)(b) = 6+72= 78m< 80m

(1A)(c) t = 0.2 5 s =a = 030

50.2 = 6.25ms2 (1M+1A) = 6.25ms2


6 90 m P Q 5ms1

(a) P (2)(b) P (i) Q (2)(ii) Q (2)

B

. . . . (a)

suatv s = ut + 1

2at 2

s = ut + 12

at 2

90= 0+ 12

(9.81)t 2P (1M)

tP = 4.284 4.28 s (1A)uatvs v = u+at

(b) (i) v = u+atvQ = 5+ (9.81)(4.284)=37.0237.0ms1 (1M+1A) Q 37.0ms1

uatvs s = ut + 1

2at 2 v2u2 = 2as

(ii) s = ut + 12

at 2

sQ = (5)(4.284)+1

2(9.81)(4.284)2 =68.58m (1M)

= 9068.58 21.4m (1A) v2u2 = 2as(37.02)252 = 2(9.81)sQ sQ =68.58m = 9068.58 21.4m

P Q


7

A. N mg

R

T

F = fF < fF > f

f

F = f < fmax

F f = fmax


7


Rmg


7B.

V

V

V


C. i 1

2

3 F =ma

4

(a) (3)(b) (1)

(a) =

A(2A)

F F (1A)(b) (1A)


7 500 g

(a) (2)(b) (i) t = 0 1.0 s(ii) t = 1.0 1.6 s(iii) t = 1.6 2.0 s(3)

(a)

(2A)T =mg = A(b) . . vt a . F =ma . (i) a1 = 0.50

10 = 0.5ms2T1mg =ma1 T1 = (0.5)(0.5+9.81)= 5.155N (1A)(ii) a2 = 0T2mg =ma2 T2 = (0.5)(9.81)= 4.905N (1A)(iii) a3 = 00.5

21.6 =1.25ms2T3mg =ma3 T3 = (0.5)(1.25+9.81)= 4.28N (1A)


600 g 2 s 10ms1(a) (3)(b) 2 s (3)(c) (i) (1)(ii) (1)

(a) (1A) (1A) (1A)(b) . . F =ma .

a = v ut

= 1002

= 5ms2 (1M)

F =mg =

F mg =maF =ma+mg = (0.6)(5)+ (0.6)(9.81)= 8.886N (1M+1A)(c) (i) v = 0

(1A)(ii) = 0 = (1A)


8

B

A.


8

J = F d = F sin Nm

Y

mg


B. y

y

V a

V

AL-- Q AB C

V


8C. i 1

2

3 F =ma

4

1

2

3 F =ma

4

AB C C A B 6 kg C 4 kg 5N(a) (2)(b) (4)

(a) mC g f A fB = (mA +mB +mC )a

(4)(9.81)55= (6+6+4)a (1M)a = 1.8275ms2 (1A)(b) ATAB = A B

TAB f A =mA aTAB 5= (6)(1.8275) (1M)

TAB 16.0N (1A) CTBC = B C

mC g TBC =mC a(4)(9.81)TBC = (4)(1.8275) (1M)

TBC 31.9N (1A) C A B


F B A B 30 1ms1A B 250 g 500 g(a) B R F (4)(b) A B f (2)(a) .

. . F =ma .

B B F

R = BM g =(M =mA +mB )

y RM g cos30= 0R =M g cos30 = (0.25+0.5)(9.81)cos30 6.37N (1M+1A)x F M g sin30=M aF =M a+M g sin30 = (0.25+0.5)(1)+ (0.25+0.5)(9.81)sin30 4.43N

(1M+1A)(b) . . . F =ma .

A B B

fB A = B AmA g = ARB A = B A

x fB A mA g sin30=mA afB A =mA a+mA g sin30 = (0.25)(1)+ (0.25)(9.81)sin30 1.48N (1M)A B 1.48Nx (1A)

R f R f ( = 0)


8 2 kgOA 12 N P B 4 NQO A 0.25m(a) OB (2)(b) O (2)(c) A B

(2)

(a) = 0O

=4dOB = (12)(0.25) (1M)

dOB = 0.75m (1A)(b) = 0T = 12+2+4= 18N (1M+1A)(c) A

=(4)(0.25+0.75)+ (2)(0.25)= TB (0.25+0.75)

TB = 4.5N (1A) B

TATA +TB = 18 TA = 184.5= 13.5N (1A) (a)


9

A. W

= F -s W = W = F s cos J = 90 F sW = 0

(KE) KE = KE = 12

mv2


9 (PE)

= KE + PE PE = PE =mg h

=


EPE

EL

P P = P = Et= W

t W J s1 P = F v


9B.

CE-- Q

V

V CE-- Q

V v P = F v


C. i 1

2

3

4

0.5 kg 2ms1 A BC DA D 2m 1m

(a) A C (3)(b) A D(i) (1)(ii) (1)(iii) (1)

(a) A B PE KE B C KE PE

A B (1A) B C (1A) (1A)

1

2m(v A vD )2 =

1

2mv A

2 12

mvD2(b) (i) = 1

2mv A

2 12

mvD2 = 1

2(0.5)(2)20= 1 J (1A)(ii) =mg (hA hD )= (0.5)(9.81)(21)= 4.905 J (1A) F AD

W = F s(iii) = + = 4.095+1= 5.905 J (1A) C C


9 250 kg 20 m 30 kg 2m

(a) (2)(b) (2)(a)

v2u2 = 2as=

1

2M v

2 =M g h11

2v2 = (9.81)(20) (1M)

v 19.8ms1 (1A) 19.8ms1(b) F

F =+F s = [M g (h1+h2)+mg h2]+0

F (2)= (250)(9.81)(20+2)+ (30)(9.81)(2) (1M)

F 27300N (1A) ( v2 h)


10ms120N 100 kg

(a) (2)(b) (1)(c) 5 s 10 ms1 20 ms1 (4)

(a) v F P = F v PP = F v = (20)(10)= 200W (1M+1A)(b) (1A)(c) P = W

t= F s

t P

a = v u

t= 2010

5= 2ms2

F = f =F f =ma F =ma+ f = (100)(2)+20= 220N (1M)s = ut + 1

2at 2 = (10)(5)+ 1

2(2)(5)2 = 75m (1M)

P = W

t= F s

t= (220)(75)

5= 3300W (1M+1A)

(a) a = 0 F = f =

P v


10

A. p p =mv kgm s1 = F =ma =m (v u

t

)= mv mu

t

= Ft = F t p =mv mu = F t N s kgm s1

t F


= (4)(2)+ (3)(2)= 2 kgm s1 = (4)(1)+ (3)(2)= 2 kgm s1

=

mAuA +mB uB =mA v A +mB vB

B

v

= =

= >


10

A B B x y

uB = 0mA =mB A+B = 90 B


B.

V

V

AL-- Q

V


10C. i 1

2

3

1600 kg F t (a) (2)(b) (2)(c)

Ft (2)(a) = Ft

12

(30.5)(1.8104) = 22500 kgm s1m

0

v mu = 225001600u = 22500 (1M)

u 14.1ms1 (1A) 14.1ms1(b) = = 2250030.5 = 9000N (1M+1A)

AA

(c)

(2A)

(b)


2 kg 100 g150ms1(a) (i)

(2)(ii) (2) AL--B Q(b)(b) (3)

(a) (i)

(1A) (1A)(ii) (1A) (1A)(b)

mAuA +mB uB = (mA +mB )v

(0.1)(150)+0= (0.1+2)v

v = 7.143ms1 (1M)

== 12

(mA +mB )v2

= 12

(0.1+2)(7.143)2 (1M)

= 53.57 53.6 J (1A) (b)


10 1.5 kg0.5 kg 2ms1 15 2ms1 30 0.02 s

(a) (3)(b) (2)(c) (2)(a) x y

xmAuA =mA v A cosA +mB vB cosB

(1.5)(2)= (1.5)v A cos15+ (0.5)(2)cos30 (1M)

v A = 1.473 1.47ms1 (1A) 1.47ms1

(b) F = mB vB mB uB

t= (0.5)(2)0

0.02= 50N (1M)

50N (1A)(c) = 1

2mAuA

2+ 12

mB

0

uB2 = 1

2(1.5)(2)2 = 3 J (1M)

= 1

2mA v A

2+ 12

mB vB2 = 1

2(1.5)(1.473)2+ 1

2(0.5)(2)2 2.63 J (1M)

(1A) 30


11

A. B

x y t

vx

x = ux t vx = ux

ay =g

y = uy t + (g )t 2

vy = uy + (g )t


11

B

=

T 0= uy + (g )

(T

2

)

uy = g(

T

2

)

H 0uy 2 = 2(g )H

uy 2 = 2g H

(90)

60 = 9030

R R = ux T uy = g

(T

2

)

R = 2ux uyg

= 45


B.

V

V F

AL-- Q

V


11C. i 1

2

3

A B 2m C h A 1m(a) B (2)(b) (2)(c) h (2)(a) v

= 1

2mv

2 =mg h

v =

2g h =p2(9.81)(1)= 4.429 4.43ms1 (1M+1A)(b) t

+x+y

x = ux t T = x

ux= 2

4.429= 0.4515 0.452 s (1M+1A)(c) y = uy t + 1

2(g )t 2

B uy = 0 = 4.43ms1y = 0+ 1

2(9.81)(0.4515)2 =1m (1M)

h = 1m (1A) B ( uy > 0)


10 ms1 30 5 m A B 5 m C D E

(a) B (3)(b) BD (3)(c) E (2)

+x+y

(a) Aux = u cos = 10cos30 = 8.660ms1 (1M) B C

vy2uy 2 = 2(g )s

0uy 2 = 2(9.81)(5)

uy = 9.905ms1 (1M) B u =

ux 2+uy 2 =

p8.6602+9.9052 = 13.16 13.2ms1 (1A)(b) B D

y = uy t + 12

(g )t 2

0= 9.905t + 12

(9.81)t 2 t = 1.421 1.42 s (1M) t = 0 x = ux t = (8.660)(1.421) 12.3m (1M+1A)(c) A C = 0

C E = 0 A C = C E 1

2mv A

2 12mvC

2 =mg hC mg hE1

2(10

2) 1

2(8.660

2)= (9.81)(5) (9.81)(hE ) (1M)

hE 3.73m (1A) E


11 (a) A 20 ms1 40 B 38 m

(i) (2)(ii) B (3)(b) B 16 ms1 1.8m B (2)

(a) (i)

+x+y

vy

2uy 2 = 2(g )s

0 (20sin40)2 = 2(9.81)H (1M)

H 8.42m (1A)(ii) t

x = ux t

38= (20cos40)t

t = 2.480 2.48 s (1M)

y = uy t +1

2(g )t 2

= (20sin40)(2.480)+ 12

(9.81)(2.480)2 (1M)

1.71m (1A)(b)

=

mg h =1

2mu

2 12mv

2

(9.81)(1.8)= 12

u2 12

(16)2 (1M)

u 17.1ms1 (1A) A 50(a)(ii) (90)


12

A. = = s

r rad = x180

0 112

1

8

1

6

1

4

1

21

0 30 45 60 90 180 360 0

6

4

3

2 2

=

= t rad s1 s1

T = = 2T

= vr


12 a a =

a = t ms2 a = v2r= r2

FF F = F =ma = mv2

r=mr2

v a F


B.

V

V

V


12C. i 1

2

3 =mv2/rmr2

4

1200 kg 25ms1 200m (4).

B

R =mg = (1A) & . =mv2/r = 0

R sin = mv2

r(1) (1M)

R cos =mg (2) (1M).

tan = sincos

v = 25ms1g = 9.81ms2r = 200m()/(): R sin

R cos=mv

2

r 1mg

tan = v2

g r= 25

2

(9.81)(200)

17.7 (1A)


0.2 kg 0.8m 30 T (4)

.

T =mg = & . =mv2/r = 0

T sin =m

L sin

r2

T =mL2 (1) (1M)

T cosmg = 0

T cos =mg (2) (1M)

. g = 9.81ms2L = 0.8m = 30m = 0.2 kgT()/(): T

T cos=mL

2

mg

=

g

L cos=

9.81

0.8cos30= 3.763 3.76 rad s1 (1A)

T =mL2 = (0.2)(0.8)(3.763)2 2.27N (1A) T


13

A. =

F = GMm

r 2 G = 6.671011 Nm2 kg2

g g = g = F

m= GM

r 2 Nkg1

GMm

r 2= mv

2

r GMm

r 2=mr2


B.

V

V r g = 9.81ms2

V r


13C.

1000 kg(a)

3.82108 m

(i) (2)(ii) (1)(b) 100m 20ms1 (3)

= 5.971024 kg = 7.351022 kg = 1.74106 m(a) (i)

FE = GMEmr 2

= (6.671011) (5.971024)1000

[0.5 (3.82108)]2 = 10.92N (1M)FM = GMMm

r 2= (6.6710

11) (7.351022)1000[0.5 (3.82108)]2 = 0.1344N

(1M)(ii) F = FEFM = 10.920.1344 10.8N (1A)(b) =

gM = GMM

RM2 = (6.671011) (7.351022)(1.74106)2 = 1.619ms2 (1M) s = ut + 1

2at 2

100= 20t + 12

(1.619)t 2 t 4.26 s 28.8 s (1M+1A) (b)


24 = 6.37106 m(a) (2)(b)

(1)(c) (4)(a)

A

(2A)(b) (1A)(c) GMm

r 2=mr2

GMm

r 2=mr

(2

T

)2

r =(

GMT 2

42

) 13

(1M)

g = GM

RE2 GM = g RE2 (1M) (M)

r =(

g RE2T 242

) 13[

(9.81)(6.37106)2(246060)242

] 13

= 4.222107 m(1M)

h = r RE = (4.222107) (6.37106) 3.59107 m (1A) 12 T r

1348660483 Studyguide 2 CHI Gray

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