Question 1

A uniform beam is balanced horizontally on a fulcrum placed at its center. If a mass $$m is $$hung at a distance $$d$$ from the left end, at what distance from the right end should a mass $$2m be $$hung to maintain equilibrium? (Assume the beam's mass is negligible.)

Accepted Answer

$$\frac{d}{2}$$

Question 2

A gymnast of mass $$50\ \mathrm{kg}$$ stands on a balance beam $$5\ \mathrm{m}$$ long. If she stands $$1\ \mathrm{m}$$ from the left end, where should a $$25\ \mathrm{kg}$$ counterweight be placed from the right end to keep the beam balanced? (Assume the beam is uniform and massless.)

Accepted Answer

$$2\ \mathrm{m}$$

Question 3

A $$0.2\ \mathrm{kg}$$ baseball moving at $$40\ \mathrm{m/s} is $$hit by a bat and leaves in the opposite direction at $$60\ \mathrm{m/s}. $$What is the impulse delivered to the ball by the bat?

Accepted Answer

$$20\ \mathrm{kg\cdot m/s}$$

Question 4

A $$1000\ \mathrm{kg}$$ car traveling east at $$20\ \mathrm{m/s}$$ collides perfectly inelastically with a $$1500\ \mathrm{kg}$$ truck traveling north at $$10\ \mathrm{m/s}. $$What is the magnitude of the velocity of the combined wreck immediately after the collision?

Accepted Answer

$$13.3\ \mathrm{m/s}$$

Question 5

A figure skater spins with arms extended, then pulls her arms in close to her body. Which of the following best describes what happens to her angular velocity and angular momentum?

Accepted Answer

Angular velocity increases; angular momentum remains constant.

Question 6

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$0.5\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is its angular momentum about the center?

Accepted Answer

$$8\ \mathrm{kg\cdot m^2$/s}$$

Question 7

A $$0.5\ \mathrm{kg}$$ ball is dropped from a height of $$10\ \mathrm{m}. $$Neglecting air resistance, what is the ball's speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$14\ \mathrm{m/s}$$

Question 8

A $$60\ \mathrm{kg}$$ diver jumps off a $$3\ \mathrm{m}$$ platform. What is her kinetic energy just before hitting the water? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$1764\ \mathrm{J}$$

Question 9

A $$5\ \mathrm{kg}$$ block slides down a frictionless incline $$4\ \mathrm{m}$$ high. What is its speed at the bottom?

Accepted Answer

$$8.9\ \mathrm{m/s}$$

Question 10

A $$0.1\ \mathrm{kg}$$ bullet is fired at $$500\ \mathrm{m/s}$$ into a $$2\ \mathrm{kg}$$ block at rest on a frictionless surface. If the bullet embeds in the block, what is their final velocity?

Accepted Answer

$$20\ \mathrm{m/s}$$

Question 11

A $$3\ \mathrm{kg}$$ object is moving at $$6\ \mathrm{m/s}. $$How much work is required to bring it to rest?

Accepted Answer

$$54\ \mathrm{J}$$

Question 12

A $$10\ \mathrm{kg}$$ box is pushed up a $$30^\circ$$ incline for $$5\ \mathrm{m} at $$constant speed. If the coefficient of kinetic friction is $$0.2$$, what is the total work done by the applied force? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$392.7\ \mathrm{J}$$

Question 13

A $$0.5\ \mathrm{kg}$$ mass attached to a spring oscillates with amplitude $$0.1\ \mathrm{m}$$ and maximum speed $$2\ \mathrm{m/s}. $$What is the spring constant $$k$$?

Accepted Answer

$$400\ \mathrm{N/m}$$

Question 14

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$0.5\ \mathrm{m} at$$ $$4\ \mathrm{m/s}. $$What is the magnitude of the centripetal force?

Accepted Answer

$$32\ \mathrm{N}$$

Question 15

A $$0.2\ \mathrm{kg}$$ puck slides on frictionless ice at $$3\ \mathrm{m/s}$$ and collides elastically with a stationary $$0.3\ \mathrm{kg}$$ puck. What is the velocity of the $$0.2\ \mathrm{kg}$$ puck after the collision?

Accepted Answer

$$1.2\ \mathrm{m/s}$$

Question 16

A $$1\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$2\ \mathrm{m} at$$ $$4\ \mathrm{m/s}. $$What is its angular momentum?

Accepted Answer

$$8\ \mathrm{kg\cdot m^2$/s}$$

Question 17

A $$0.5\ \mathrm{kg}$$ mass is attached to a spring with $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$0.314\ \mathrm{s}$$

Question 18

A $$2\ \mathrm{kg}$$ block slides at $$5\ \mathrm{m/s} on a $$frictionless surface and collides with a $$3\ \mathrm{kg}$$ block at rest. If they stick together, what is their final velocity?

Accepted Answer

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

Question 19

A $$0.5\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$What is the maximum height reached? (Neglect air resistance, $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$5.1\ \mathrm{m}$$

Exam 4 Review: Equilibrium, Elasticity, Momentum, and Energy

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