Q: A wire that has length $$3.20\ \mathrm{m}$$ and cross-sectional area $$2.00 \times 10$$^{-6}$$\ \mathrm{m^2$} is $$stretched by a downward force of $$5.00\ \mathrm{N}. If $$the wire is stretched by $$4.00 \times 10$$^{-4}$$\ \mathrm{m}$$, what is the value of Young's modulus for the material of the wire?

$$2.0 \times 10$$^{10}$$\ \mathrm{N/m^2$}$$

Question 1

Two spheres, solid cylinders, or other rigid objects of the same mass but different radii are released from rest at the same height on an inclined plane. They roll without slipping. Which of the following statements is correct?

Accepted Answer

The object with the smaller moment of inertia relative to its mass will reach the bottom first.

Question 2

A uniform disk with mass $$40\ \mathrm{kg}$$ and radius $$R = 0.500\ \mathrm{m} is $$mounted on an axle through its center. If a net torque of $$20.0\ \mathrm{N \cdot m} is $$applied, what is the angular acceleration $$\alpha of $$the disk?

Accepted Answer

$$2.00\ \mathrm{$$rad/s^2$$}$$

Question 3

A solid sphere of mass $$2.0\ \mathrm{kg}$$ and radius $$0.10\ \mathrm{m}$$ rolls without slipping on a horizontal surface. What fraction of its total kinetic energy is rotational?

Accepted Answer

$$\frac{2}{7}$$

Question 4

A block with mass $$0.40\ \mathrm{kg} is $$attached to a horizontal spring that has force constant $$k = 8.00\ \mathrm{N/m}. $$The block is moving in simple harmonic motion on a frictionless surface. What is the maximum acceleration of the block during its motion if the amplitude is $$0.040\ \mathrm{m}$$?

Accepted Answer

$$0.80\ \mathrm{m/s^2$}$$

Question 5

A uniform disk of radius $$R = 0.400\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A light string is wrapped around the disk and a $$2.00\ \mathrm{kg}$$ block is suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. If the block has speed $$5.00\ \mathrm{m/s}$$ after it has descended $$2.00\ \mathrm{m}$$, what is the moment of inertia of the disk for rotation about the axle?

Accepted Answer

$$0.250\ \mathrm{kg \cdot m^2$}$$

Question 6

A solid disk with radius $$0.200\ \mathrm{m} is $$mounted on an axle through its center. It has moment of inertia $$I$$ and starts to rotate with constant angular acceleration $$\alpha = 2.00\ \mathrm{$$rad/s^2$$}. $$What is the tangential component of the acceleration of a point on the rim of the disk after $$4.00\ \mathrm{s}$$?

Accepted Answer

$$0.800\ \mathrm{m/s^2$}$$

Question 7

A uniform disk with mass $$40\ \mathrm{kg}$$ and radius $$R = 0.500\ \mathrm{m} is $$mounted on an axle through its center. If it starts at rest and takes $$10.0\ \mathrm{s} to $$rotate with constant angular acceleration $$\alpha = 2.00\ \mathrm{$$rad/s^2$$}$$, what is its rotational kinetic energy after it has turned through $$60.0\ \mathrm{rad}$$?

Accepted Answer

$$600\ \mathrm{J}$$

Question 8

A block with mass $$0.40\ \mathrm{kg} is $$attached to a horizontal spring that has force constant $$k = 8.00\ \mathrm{N/m}. $$The block is moving in simple harmonic motion on a frictionless surface. When the block is at $$x = 0.040\ \mathrm{m}$$, it has speed $$0.60\ \mathrm{m/s}. $$What is the amplitude of the motion of the block?

Accepted Answer

$$0.076\ \mathrm{m}$$

Question 9

A block with mass $$0.20\ \mathrm{kg} is $$attached to a horizontal spring that has force constant $$k = 6.00\ \mathrm{N/m}. $$The block is moving in simple harmonic motion on a frictionless surface. During its motion, what is the maximum magnitude of the force that the spring exerts on the block?

Accepted Answer

$$2.40\ \mathrm{N}$$

Question 10

A uniform disk of radius $$R = 0.500\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A light string is wrapped around the disk and a $$2.00\ \mathrm{kg}$$ block is suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. If the tension in the rope is $$4.00\ \mathrm{N}$$, what is the moment of inertia of the disk for rotation about the axle?

Accepted Answer

$$0.250\ \mathrm{kg \cdot m^2$}$$

Question 11

A uniform rod of length $$3.00\ \mathrm{m}$$ and mass $$8.00\ \mathrm{kg} is $$supported horizontally by a wall by frictionless hinges. The rod is held at rest at an angle of $$30^\circ$$ with the horizontal. What is the vertical component of the hinge force at the wall?

Accepted Answer

$$39.2\ \mathrm{N}$$

Question 12

A block is attached to a horizontal spring and moves in simple harmonic motion with frequency $$5.00\ \mathrm{Hz}. If $$the amplitude of the motion is changed to $$0.125\ \mathrm{m}$$, what is the new frequency of the motion?

Accepted Answer

$$5.00\ \mathrm{Hz}$$

Question 13

A uniform disk of radius $$R = 0.400\ \mathrm{m} is $$mounted on a horizontal frictionless axle at its center. A light string is wrapped around the disk and a $$2.00\ \mathrm{kg}$$ block is suspended from the free end of the string. The system is released from rest and the block moves downward as the disk rotates. What is the acceleration of the block?

Accepted Answer

$$6.53\ \mathrm{m/s^2$}$$

Question 14

A uniform rod of length $$3.00\ \mathrm{m}$$ and mass $$8.00\ \mathrm{kg} is $$supported horizontally by a wall by frictionless hinges. The rod is held at rest at an angle of $$30^\circ$$ with the horizontal. What is the minimum coefficient of friction at the floor required for the ladder not to slip?

Accepted Answer

$$0.577$$

Question 15

A wire that has length $$3.20\ \mathrm{m}$$ and cross-sectional area $$2.00 	imes 10$$^{-6}$$\ \mathrm{m^2$} is $$stretched by a downward force of $$5.00\ \mathrm{N}. If $$the wire is stretched by $$4.00 	imes 10$$^{-4}$$\ \mathrm{m}$$, what is the value of Young's modulus for the material of the wire?

Accepted Answer

$$2.0 	imes 10$$^{10}$$\ \mathrm{N/m^2$}$$

Question 16

On a planet other than earth, a simple pendulum with length $$0.50\ \mathrm{m}$$ has a frequency of $$0.70\ \mathrm{Hz}. $$What is the value of $$g on $$this planet?

Accepted Answer

$$9.7\ \mathrm{m/s^2$}$$

Physics Exam 3 Study Guidance: Rotational Motion, Oscillations, and Equilibrium

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