Question 1

A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope?

Accepted Answer

$$24\ \mathrm{m/s}$$

Question 2

A force on a particle depends on position such that $$F(x) = (3.00\ \mathrm{N/m}^2)x^2$ + (6.00\ \mathrm{N/m})x$$ for a particle constrained to move along the x-axis. What work is done by this force on a particle that moves from $$x = 0.00\ \mathrm{m} to$$ $$x = 2.00\ \mathrm{m}$$?

Accepted Answer

$$48.0\ \mathrm{J}$$

Question 3

A ball of mass $$m is $$attached to a string and swings in a vertical circle of radius $$r. $$What is the tension force in the string at the lowest point of its swing?

Accepted Answer

$$2mg$$

Question 4

A particle moves along the x-axis while acted on by a single conservative force parallel to the axis. The force corresponds to the potential-energy function $$U(x)$$ graphed below. The particle is released from rest at point A. What is the direction of the force on the particle at point A?

Accepted Answer

-x

Question 5

Given the potential energy function $$U(x)$$ shown, at what value or values of $$x$$ correspond to points of stable equilibrium?

Accepted Answer

$$0.75, 1.8$$

Question 6

An object moves from the origin to the point $$\vec{r} = 13\ \mathrm{m}\ \hat{i} + 11\ \mathrm{m}\ \hat{j}$$ under a constant force $$\vec{F} = 3\ \mathrm{N}\ \hat{i} + 5\ \mathrm{N}\ \hat{j}. $$What is the work done by the force?

Accepted Answer

$$266\ \mathrm{J}$$

Question 7

The potential energy of a body of mass $$m is $$given by $$U = -mgx - \frac{1}{2}kx^2$. The corresponding force is:

Accepted Answer

$$-mg - kx$$

Question 8

The iron ball shown is being swung in a vertical circle at the end of a $$0.7\ \mathrm{m}$$ long string. How slowly can the ball go through its top position without having the string go slack?

Accepted Answer

$$1.3\ \mathrm{m/s}$$

Question 9

A kicker's foot was in contact with a football for $$0.051\ \mathrm{s}$$, and the average force exerted was $$470\ \mathrm{N}. $$What was the impulse delivered to the ball?

Accepted Answer

$$11\ \mathrm{Ns}$$

Question 10

A bullet of mass $$m = 2.0\ \mathrm{g} is $$fired and hits a wooden block of mass $$M = 0.50\ \mathrm{kg}$$ with approximately horizontal velocity $$v = 100\ \mathrm{m/s} to $$the right. The bullet becomes instantaneously embedded in the block. The block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic friction $$\mu_k = 0.35. $$What is the horizontal velocity of the center of mass of the bullet-block system right after the collision?

Accepted Answer

$$0.39\ \mathrm{m/s}$$\ to\ the\ right$

Question 11

How far does the block slide after the collision before it comes to rest? (Assume $$\mu_k = 0.35$$ and $$v_0 = 0.39$$\ \mathrm{m/s}$$)

Accepted Answer

$$4.8\ \mathrm{cm}$$

Question 12

A car slides at a speed of $$10\ \mathrm{m/s}$$ into a curve. The actual frictional force between the tires and slippery road has a magnitude of $$900\ \mathrm{N}. $$The car:

Accepted Answer

slides off to the outside of the curve

Question 13

A crate moves $$10\ \mathrm{m} to $$the right on a horizontal surface as a woman pulls on it with a $$10\ \mathrm{N}$$ force. Rank the situations shown below according to the work done by her, least to greatest.

Accepted Answer

1, 2, 3

Question 14

A $$4.0\ \mathrm{kg}$$ block begins sliding on a rough surface. Two seconds after it begins sliding, a horizontal, time-dependent force is applied to the mass. The force is removed eight seconds later. The graph shows how the force on the block varies with time. What is the magnitude of the total impulse of the force acting on the block?

Accepted Answer

$$24\ \mathrm{Ns}$$

Question 15

A block of mass $$m is $$projected with a velocity $$v_i = 1.2\ \mathrm{m/s}$$ upon separation from a spring. The block descends a ramp and has a velocity $$v_f = 1.9\ \mathrm{m/s} at $$the bottom. The track is frictionless between points A and B. Which conservation law(s) apply to the system between point A and B after the $$81\ \mathrm{N}$$ force is removed, and why?

Accepted Answer

Conservation of energy only, because no external forces act

Question 16

A large wedge with a mass of $$10\ \mathrm{kg}$$ rests on a horizontal frictionless surface. A block with a mass of $$5.0\ \mathrm{kg}$$ starts from rest and slides down the inclined surface of the wedge, which is rough. At one instant the vertical component of the block's velocity is $$3.0\ \mathrm{m/s}$$ and the horizontal component is $$6.0\ \mathrm{m/s}. $$Which conservation law(s) apply to the box-wedge system as the box slides down the wedge and why?

Accepted Answer

Conservation of momentum in the horizontal direction only, because the surface is frictionless

Question 17

A block of mass $$m$$ slides down a ramp of height $$h$$ and length $$L$$ with friction coefficient $$\mu. $$What is the final speed of the block at the bottom of the ramp?

Accepted Answer

$$\sqrt{2g(h-\mu L)}$$

Question 18

A $$2.0\ \mathrm{kg}$$ block is attached to a spring with spring constant $$k = 81\ \mathrm{N/m}. $$The block is compressed $$x = 0.5\ \mathrm{m}$$ from equilibrium and released. What is the elastic potential energy stored in the spring before release?

Accepted Answer

$$20.25\ \mathrm{J}$$

Practice Questions and Concepts in College Physics: Mechanics, Energy, and Dynamics

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