Question 1

A car moves in a circle of radius $r$ at constant speed $v$. What is the direction of the centripetal acceleration?

Accepted Answer

Radially inward toward the center

Question 2

Two small objects, with masses $m$ and $M$, are originally a distance $r$ apart, and the gravitational force on each has magnitude $F$. If the second object has its mass changed to $2M$, and the distance is changed to $r/4$, what is the magnitude of the new gravitational force?

Accepted Answer

$32F$

Question 3

A uniform solid cylinder of mass $10\,\mathrm{kg}$ can rotate about a frictionless axle through its center. A rope wrapped around the outer radius $R_1 = 1.0\,\mathrm{m}$ exerts a force of magnitude $F_1 = 5.0\,\mathrm{N}$ to the right. A second rope wrapped around another section of radius $R_2 = 0.50\,\mathrm{m}$ exerts a force of magnitude $F_2 = 6.0\,\mathrm{N}$ downward. What is the angular acceleration of the cylinder? ($I_{\mathrm{cylinder}} = \frac{1}{2}MR^2$)

Accepted Answer

$1.0\,\mathrm{rad/s^2}$

Question 4

A 1.5-kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the magnitude of the minimum force, applied 0.30 m on the other side of the pivot, that is needed to make the child lift off the ground?

Accepted Answer

$75\,\mathrm{N}$

Question 5

A pulley has an initial angular speed of $12.5\,\mathrm{rad/s}$ and a constant angular acceleration of $3.41\,\mathrm{rad/s^2}$. Through what angle does the pulley turn in $5.26\,\mathrm{s}$?

Accepted Answer

$122\,\mathrm{rad}$

Question 6

A 3.0-m-long ladder, weighing $200\,\mathrm{N}$, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of $1.00\,\mathrm{m}$ away from the wall. The ladder is not completely uniform, so its center of gravity is $1.0\,\mathrm{m}$ from its base. What force of friction must the floor exert at the base of the ladder to prevent the ladder from sliding down?

Accepted Answer

$93.3\,\mathrm{N}$

Question 7

A 1.0-kg mass is located at $(0.0\,\mathrm{m}, 8.0\,\mathrm{m})$, and a 1.0-kg mass is located at $(12.0\,\mathrm{m}, 0.0\,\mathrm{m})$. You want to add a 4.0-kg mass so that the center of mass (or center of gravity) of the three-mass system will be at the origin. What should be the coordinates of the 4.0-kg mass?

Accepted Answer

$(0.0\,\mathrm{m}, 0.0\,\mathrm{m})$

Question 8

A drive chain in a bicycle is applying a torque of $0.850\,\mathrm{N \cdot m}$ to the wheel of the bicycle. You can treat the wheel as a thin uniform hoop (or ring) with a mass of $0.750\,\mathrm{kg}$ and a radius of $33.0\,\mathrm{cm}$. What is the angular acceleration of the wheel?

Accepted Answer

$4.13\,\mathrm{rad/s^2}$

Question 9

A 20-m piano wire has a radius of $0.50\,\mathrm{mm}$. One end is fixed and the other is wrapped around a tuning peg, which has a diameter of $3.5\,\mathrm{mm}$ and is $80\,\mathrm{cm}$ away. After the wire just becomes taut, the peg is given three full turns. What is the tension in the wire? Young's modulus for steel is $2.0 	imes 10^{11}\,\mathrm{N/m^2}$.

Accepted Answer

$6.5\,\mathrm{kN}$

Question 10

A store's sign has a mass of $20\,\mathrm{kg}$ and is $3.0\,\mathrm{m}$ long. It is uniform, so its center of gravity is at the center of the sign. It is supported horizontally by a small loose bolt attached to the wall at one end, and by a wire at the other end, as shown in the figure. What is the tension in the wire?

Accepted Answer

$320\,\mathrm{N}$

Question 11

A man in a gym is holding an $8.0\,\mathrm{kg}$ weight at arm's length, a distance of $0.55\,\mathrm{m}$ from his shoulder joint. What is the torque about his shoulder joint due to the weight if his arm is held at $30^\circ$ below the horizontal?

Accepted Answer

$37\,\mathrm{N \cdot m}$

Question 12

A 1.0-m-high refrigerator has a mass of $20\,\mathrm{kg}$ and is $1.0\,\mathrm{m}$ long. Its center of gravity is at the center of the sign. If it is supported horizontally by a small loose bolt attached to the wall at one end, and by a wire at the other end, as shown in the figure. What is the tension in the wire?

Accepted Answer

$1.6\,\mathrm{m}$

Question 13

A light ideal spring stretches by $21.0\,\mathrm{cm}$ when it is used to hang a $135\,\mathrm{N}$ object. What is the weight of a piece of electronic equipment that would stretch the spring by $4.4\,\mathrm{cm}$ if you hang the equipment using the spring?

Accepted Answer

$28\,\mathrm{N}$

Question 14

A compact disc is rotating at $210\,\mathrm{rpm}$. What is its angular speed in rad/s?

Accepted Answer

$22\,\mathrm{rad/s}$

Question 15

When a fan is turned off, its angular speed decreases from $10.0\,\mathrm{rad/s}$ to $6.3\,\mathrm{rad/s}$ in $5.0\,\mathrm{s}$. What is the magnitude of the average angular acceleration of the fan?

Accepted Answer

$0.74\,\mathrm{rad/s^2}$

Question 16

An irregularly shaped object that is $10\,\mathrm{m}$ long is placed with each end on a scale. If the scale on the right reads $4\,\mathrm{N}$ while the scale on the left reads $7\,\mathrm{N}$, how far from the left end is the center of gravity of this object?

Accepted Answer

$4.7\,\mathrm{m}$

Question 17

A 4.0-kg mass is located at $(0.0\,\mathrm{m}, 0.0\,\mathrm{m})$, a 1.0-kg mass is located at $(0.0\,\mathrm{m}, 8.0\,\mathrm{m})$, and a 1.0-kg mass is located at $(12.0\,\mathrm{m}, 0.0\,\mathrm{m})$. What are the coordinates of the center of mass of the system?

Accepted Answer

$(2.0\,\mathrm{m}, 1.6\,\mathrm{m})$

Fundamental Concepts and Problem Solving in College Physics

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