Q: A 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 $$2.0 \times 10$$^{11}$$~\mathrm{N/m^2$}.$$

$$1.3 \times 10^3$~\mathrm{N}$$

Question 1

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

Accepted Answer

Directly toward the center of its circular path

Question 2

Two small objects, with masses $$m$$ and $$M$$, are originally a distance $$r$$ apart. If the second object's mass is changed to $$2M$$, and the distance is changed to $$r/4$$, what is the magnitude of the new gravitational force between them?

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 $$(12~\mathrm{m},~0.0~\mathrm{m}). $$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

$$(3.0~\mathrm{m},~-8.0~\mathrm{m})$$

Question 4

At a certain instant, a compact disc is rotating at 210 rpm. What is its angular speed in rad/s?

Accepted Answer

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

Question 5

When a fan is turned off, its angular speed decreases from $$10~\mathrm{rad/s} to$$ $$6.3~\mathrm{rad/s} in$$ $$5.0~\mathrm{s}. $$What is the magnitude of the average angular acceleration of the fan?

Accepted Answer

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

Question 6

An old LP record that is originally rotating at $$33.3~\mathrm{rad/s} is $$given a uniform angular acceleration of $$2.15~\mathrm{$$rad/s^2$$}. $$Through what angle has the record turned when its angular speed reaches $$72.0~\mathrm{rad/s}$$?

Accepted Answer

$$948~\mathrm{rad}$$

Question 7

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 8

The drive chain in a bicycle is applying a torque of $$0.850~\mathrm{N \cdot m} to $$the wheel. 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

$$3.43~\mathrm{$$rad/s^2$$}$$

Question 9

A uniform solid cylinder of mass $$10~\mathrm{kg}$$ can rotate about a frictionless axle through its center $$O. A $$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

$$0.40~\mathrm{$$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 electronic equipment that would stretch the spring by $$4.7~\mathrm{cm} if $$you hang the equipment using the spring?

Accepted Answer

$$30~\mathrm{N}$$

Question 11

A $$120~\mathrm{kg}$$ refrigerator that is $$2.0~\mathrm{m}$$ tall and $$85~\mathrm{cm}$$ wide has its center of mass at its geometrical center. You are attempting to slide it along the floor by pushing horizontally on the side. What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

Accepted Answer

$$1.6~\mathrm{m}$$

Question 12

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

$$300~\mathrm{N}$$

Question 13

A $$3.00~\mathrm{m}-$$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 $$1.20~\mathrm{m}$$ from its base. What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down?

Accepted Answer

$$150~\mathrm{N}$$

Question 14

A $$15~\mathrm{kg}$$ child is sitting on a playground teeter-totter, $$1.5~\mathrm{m}$$ from the pivot. What is the magnitude of the minimum force, applied $$0.30~\mathrm{m} on $$the other side of the pivot, that is needed to make the child lift off the ground?

Accepted Answer

$$75~\mathrm{N}$$

Question 15

A 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

$$1.3 	imes 10^3$~\mathrm{N}$$

Question 16

A $$15~\mathrm{kg}$$ child is sitting on a playground teeter-totter, $$1.5~\mathrm{m}$$ from the pivot. What is the minimum distance, on the other side of the pivot, such that a $$220~\mathrm{N}$$ force will make the child lift off the ground?

Accepted Answer

$$2.4~\mathrm{m}$$

Question 17

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 $$96~\mathrm{N}$$ while the scale on the left reads $$71~\mathrm{N}$$, how far from the left end is the center of gravity of this object?

Accepted Answer

$$7.4~\mathrm{m}$$

Question 18

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

$$122.6~\mathrm{rad}$$

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