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Chapter 5: Rigid Body Kinetics Homework

Homework H.5.D

Given: A gear of mass m and outer radius R meshes with rack A (having a mass of 2m). RackA is constrained to move along a smooth vertical guide. Treat the gear as a homogeneous disk ofradius R. Assume that the rack does not slip on the gear.

Find: Determine the acceleration of rack A when the system is released from rest. Write youranswer as a vector.

Rigid Body Kinetics Homework Problems ME 274

Problem V-63 Given: A gear of mass m and outer radius R meshes with rack A (having a mass of

2m). Rack A is constrained to move along a smooth vertical guide. Treat the gear as a homogeneous disk of radius R. Assume that the rack does not slip on the gear.

Find: Determine the acceleration of rack A when the system is released from rest.

Write your answer as a vector.

R

O

A

smooth

no slip

C g

m

2m

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Chapter 5: Rigid Body Kinetics Homework

Homework H.5.E

Given: A pulley of mass M is connected to two blocks as shown. Assume that the axle at C isfrictionless, and that the pulley can be crudely modeled as a homogeneous disk.

Find: Determine the angular acceleration of the pulley and the acceleration of each block.

Am Bm

or

irA BC

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Chapter 5: Rigid Body Kinetics Homework

Homework H.5.F

Given: A homogeneous, thin bar AB (of length L and mass m) is pinned to a block at A. Theblock has a mass of M and is constrained to move along a smooth horizontal surface. A horizontalforce F is applied to the bar’s center of mass G at an instant when the bar is vertical and at rest.

Find: Determine the angular acceleration of the bar for the instant when the force F is applied tothe bar.

Rigid Body Kinetics Homework Problems ME 274

Problem V-51 Given: A homogeneous, thin bar AB (of length L = 3 meters and mass m = 50 kg) is

pinned to a block at A. The block has a mass of M = 100 kg and is constrained to move along a smooth horizontal surface. A horizontal force F = 200 N is applied to the bar’s center of mass G at an instant when the bar is vertical and at rest.

Find: For this problem,

a) Complete the free body diagrams for the bar and the block below. b) Determine the angular acceleration of the bar for the instant when the

force F is applied to the bar.

G

B

A

F

m

L

M

g

Use the following parameters in your analysis: L = 4 m, m = 75 kg, M = 100 kg and F = 400 N.

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