FE Review – Dynamics 1/4 - University of Minnesota Duluthdzhou/FE review/01Kenematics1.pdf · FE...

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FE Review – Dynamics 1/4 By Dr. Debao Zhou Department of Mechanical & Industrial Engineering University of Minnesota Duluth 1

Transcript of FE Review – Dynamics 1/4 - University of Minnesota Duluthdzhou/FE review/01Kenematics1.pdf · FE...

Page 1: FE Review – Dynamics 1/4 - University of Minnesota Duluthdzhou/FE review/01Kenematics1.pdf · FE Review – Dynamics 1/4 ... Sections 14-17 – Kinematics – Kinetics ... – Angular

FE Review – Dynamics 1/4

By Dr. Debao Zhou

Department of Mechanical & Industrial EngineeringUniversity of Minnesota Duluth

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ReferencesWebsite: https://moodle.umn.edu/course/view.php?id=7988

FE Supplied-Reference Handbook, Page 54-61

Sections 14-17

Kinematics– Kinematics– Kinetics– Kinetics of rotational motion

Energy and work– Energy and work

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Slides Website

• Kinematics– http://www.d.umn.edu/~dzhou/01Kenematics1.pdf

• Kinetics– http://www.d.umn.edu/~dzhou/02Kinetics1.pdf

• Kinetics of rotational motion– http://www.d.umn.edu/~dzhou/03KineticsofRotational1.pdf

• Energy and work– http://www.d.umn.edu/~dzhou/04Energy1.pdf

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Page 4: FE Review – Dynamics 1/4 - University of Minnesota Duluthdzhou/FE review/01Kenematics1.pdf · FE Review – Dynamics 1/4 ... Sections 14-17 – Kinematics – Kinetics ... – Angular

Dynamics - Scope• Dynamics - Study of moving objects

• Kinematics: Motion (Position, velocity and acceleration), Independent of force P i l ki i– Particle kinematics

– Rigid body kinematics• Kinetics:

– Force and mass for translational motion (particle, body)T d t f i ti f t ti l ti (b d )– Torque and moment of inertia for rotational motion (body)

• Energy and Work– Capability of the mass to do work: All kinds of energy

• Translational motion – Position, velocity and acceleration, mass, force, friction– Momentum, impact, work, energy – And change with time

R i l i• Rotational motion – Angle, angular velocity and angular acceleration, inertia, moment (torque), friction– Angular momentum, impulse, impact, work, energy– And change with time

C bi ti f t l ti l ti d t ti l ti

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• Combination of translational motion and rotational motion – Multi-body: Instant velocity center. etc

Page 5: FE Review – Dynamics 1/4 - University of Minnesota Duluthdzhou/FE review/01Kenematics1.pdf · FE Review – Dynamics 1/4 ... Sections 14-17 – Kinematics – Kinetics ... – Angular

Position, Velocity and Acceleration

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Example -1• Problems 1-2 refer to a particle whose curvilinear motion is

represented by the equation s = 20t + 4t2 – 3t3.

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Position, Velocity and Acceleration

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Constant Acceleration

Linear motion Rotational motion

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Example -2

• A motorist is traveling at 70 km/ h when he sees a traffic light in an intersection 250 m ahead turn red. The light 's red cycle is 15 s. The

i h i i i h i hi hi lmotorist wants to enter the intersection without stopping his vehicle, just as the light turns green.

What uniform deceleration of the vehicle will just put the motorist in the intersection when the light turns green?

(A) 0.18 m/s2

(B) 0.25 m/s2

(C) 0.37 m/s2

(D) 1 3 m/s2

250 m @ Time 15 s

V 70 k / h(D) 1.3 m/s V0 = 70 km/ h

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Example -2

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Circular motion• They have the same relationship as linear system

• Relation between linear and rotation variables

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Example -3

• The position (in radians) of a car traveling around a curve is described by the following function of time (in seconds). y g ( )(t) = t3 - 2t2 - 4t + 10

What is the angular velocity at t = 3 s?(A) -16 rad/ s(B) 4 rad / s(B) - 4 rad / s(C) 11 rad/ s(D) 15 rad/ s(D) 15 rad/ s

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Example -4

• A flywheel rotates at 7200 rev/min when the power is suddenly cut off. The flywheel decelerates at a constant y yrate of 2.1 rad/s2 and comes to rest 6 min later. How many revolutions does the flywheel make before coming to rest?to rest?(A) 18 000 rev(B) 22 000 rev(B) 22 000 rev(C) 72 000 rev(D) 390 000 rev

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Example -4

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Example 5

• Rigid link AB is 12 m long. It rotates counterclockwise about point A at 12 rev/min. A thin disk with radius 1. 75 m is pinned at its center to h li k i B Th di k l k i 60 / ithe link at point B. The disk rotates counterclockwise at 60 rev/ min

with respect to point B. What is the maximum tangential velocity seen by any point on the disk?(A) 6 /(A) 6 m/s(B) 26 m/s(C) 33 m/ s(D) 45 m/s

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Example 5

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Project Motion

• TrajectoryV ti l– Vertical

acceleration Only

• Acceleration

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Example -6

• A projectile is fired from a cannon with an initial velocity of 1000 m/ s and at an angle of 30° from the horizontal. gWhat distance from the cannon will the projectile strike the ground if the point of impact is 1500 m below the point of release?point of release?(A) 8200 m(B) 67300 m(B) 67300 m(C) 78200 m(D) 90800 m

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