Question 1

A car moves in a circular path at constant speed. What is the direction of its acceleration?

Accepted Answer

Directed toward the center of its circular path

Question 2

Two small objects, with masses $$m$$ and $$M$$, are originally a distance $$r$$ apart. The gravitational force on each object 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 3.0-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 of the three-mass system will be at the origin. What should be the coordinates of the 4.0-kg mass?

Accepted Answer

$$(3.0~\mathrm{m}, -6.0~\mathrm{m})$$

Question 4

A compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

Accepted Answer

22 rad/s

Question 5

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

Accepted Answer

0.74 rad/s$$^2$$

Question 6

An LP record that is originally rotating at 3.3 rad/s is given a uniform angular acceleration of 2.15 rad/s$$^2. $$Through what angle has the record turned when its angular speed reaches 7.20 rad/s?

Accepted Answer

7.3 rad

Question 7

A gym trainer is holding an 8.0-kg weight at arm's length, a distance of 0.55 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 8

The 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

$$10.4~\mathrm{$$rad/s^2$$}$$

Question 9

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center $$O$$, as shown in the cross-sectional view in the figure. 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

0.40 rad/s$$^2$$

Question 10

A very 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 exercise equipment that would stretch the spring by $$44.9~\mathrm{cm} if $$you hung the equipment using the spring?

Accepted Answer

289 N

Question 11

A store's sign has a mass of 20 kg and is 3.0 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

200 N

Question 12

A 3.00-m-long ladder, weighing 200 N, leans against a smooth vertical wall with its base on a horizontal rough floor, a distance of 1.00 m away from the wall. The ladder is not completely vertical, so its center of gravity is 1.50 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 N

Question 13

A 15-kg child is sitting on a playground teeter-totter, 1.5 m from one side of 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 N

Question 14

A piano wire has a radius of 0.50 mm. One end is fixed and the other is wrapped around a tuning peg, which has a diameter of 3.5 mm and is 8.0 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

4.3 kN

Question 15

An irregularly shaped object that is 10 m long is placed with each end on a scale. If the scale on the right reads 5 N while the scale on the left reads 7 N, how far from the left end is the center of gravity of this object?

Accepted Answer

4.3 m

Question 16

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

Accepted Answer

113 rad

Fundamental Concepts and Problems in Classical Mechanics

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