Tutorials In Introductory Physics: Homework
Tutorials In Introductory Physics: Homework
1st Edition
ISBN: 9780130662453
Author: Lillian C. McDermott, Peter S. Shaffer
Publisher: PEARSON
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Textbook Question
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Chapter 4.3, Problem 1aT

A T-shaped board of uniform mass density has two small holes as shown. Initially, the pivot is placedthrough the right hole, which corresponds to the center of mass of the board. The board ¡s then held in place.

1. Predict the motion of the board after it is released from rest, Explain.

Chapter 4.3, Problem 1aT, A T-shaped board of uniform mass density has two small holes as shown. Initially, the pivot is

2. Check your prediction by observing the demonstration.

a. Describe the angular acceleration of the board. Explain how you can tell.

What does your answer imply about the ne, torque about the pivot? Explain.

b. Describe the acceleration of the center of mass of the board. Explain how you can tell.

What does your answer imply about the net force acting on the board? Explain.

3. Explain how your answers about net torque and net force in question 2 would change, if at all, if there is appreciable friction between the board and the pivot and the board remains at rest.

(1)

Expert Solution
Check Mark
To determine

To Predict: The motion of the board.

Answer to Problem 1aT

The board will perform a circular repetitive motion.

Explanation of Solution

Given:

Gravitational force is acting downward on the edge of the handle.

  Tutorials In Introductory Physics: Homework, Chapter 4.3, Problem 1aT , additional homework tip  1

Formula used:

  τ=r×F=r×mg

Calculation:

  τ=r×Fτ=r×mgτ=rmgsinθ(θ=90°)τ=rmg

Conclusion:

The gravitational force at the edge of the handle leads to produce torque using equation in formula. r is the distance between the edge of the handle and the pivot around which the board will rotate. Angle between r and force is 90 degree.

(2)

Expert Solution
Check Mark
To determine

To Describe: The angular acceleration of the board, acceleration of the center of mass and the net torque about the pivot.

Explanation of Solution

Given:

  τ=rmg

  Tutorials In Introductory Physics: Homework, Chapter 4.3, Problem 1aT , additional homework tip  2

Formula used:

  τ=Iα

Where, I is the moment of inertia and α is the angular acceleration.

Calculation:

From part 1, the net torque is τ=rmg

From the rotational equation of motion:

  τ=Iα

  α=dωdt

On comparing both the equations:

  τ=rmg=Iα

  α=rmgI

The center of mass of the board lies on the axis of rotation, therefore, the acceleration of the center of mass is zero.

The net torque is τ=Iα and the net force is mg .

Conclusion:

Hence, the angular acceleration is α=rmgI . The acceleration of the center of mass of the board is zero as there is no translation motion of the board.

(3)

Expert Solution
Check Mark
To determine

The effect of friction on the torque and force.

Answer to Problem 1aT

The net torque and force will be reduced due to friction in effect.

Explanation of Solution

Given:

Gravitational force is acting downward on the edge of the handle.

Formula used:

  τ=r×Ffrictional force

  Fnet=mgfrictional force

Calculation:

  τ=r×F=r×mgτ=rmgsinθμFfτ=rmgμFf

Conclusion:

The frictional force acts opposite to the motion of the object. Hence, net force and torque are reduced which eventually reduces the angular acceleration and linear acceleration.

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