Q: A block of mass $m$ slides up a frictional incline of angle $\theta$ and coefficient of kinetic friction $\mu_k$ with initial speed $v_0$. How far $d$ does it travel up the incline before coming to rest?

$d = \frac{v_0^2}{2 g (\sin \theta + \mu_k \cos \theta)}$

Question 1

A car with mass $m$ drives over a circular hill with radius $r$. What is the maximum speed $v_{max}$ the car can have at the top of the hill before losing contact with the road? (Express your answer in terms of $m$, $g$, and $r$.)

Accepted Answer

$v_{max} = \sqrt{g r}$

Question 2

Two balls, A and B, attract each other gravitationally with a force $F$. If we double both masses and double the separation between them, what is the new magnitude of the attractive force for each case?

Accepted Answer

$F$

Question 3

A satellite in circular orbit around Earth is maintained by the force of gravity between Earth and the satellite, yet no work is done on the satellite. How is this possible?

Accepted Answer

The force of gravity is perpendicular to the direction of motion.

Question 4

You throw a baseball straight up. Compare the sign of the work done by gravity while the ball goes up and while it comes down.

Accepted Answer

Negative on the way up, positive on the way down.

Question 5

When you throw a pebble straight up with initial speed $v_i$, it reaches a maximum height $H$ (with no air resistance). At what speed should you throw the pebble upward to get twice as high?

Accepted Answer

$\sqrt{2} v_i$

Question 6

A rubber ball, with an initial speed $v$, bounces off a wall and reverses its direction such that its speed is also $v$ after the bounce. Which of the following quantities of the ball are conserved?

Accepted Answer

The kinetic energy of the ball.

Question 7

Jill does twice as much work as Jack does and in half the time. Jill's power output is:

Accepted Answer

Four times Jack's power output.

Question 8

A block of mass $M$ is at rest on a frictionless surface. A dart of mass $m$ is shot horizontally and sticks to the block. If the dart's speed before collision is $v$, what is the speed of the block-dart system immediately after the collision?

Accepted Answer

$\frac{m v}{M + m}$

Question 9

A spring with spring constant $k$ is compressed a distance $x$ by a block of mass $m$ moving at speed $v$. What is the value of $k$ in terms of $m$, $v$, and $x$ if all the kinetic energy is transferred to the spring?

Accepted Answer

$k = \frac{m v^2}{x^2}$

Question 10

A car of mass $m$ is driving over a circular hill of radius $r$. What is the normal force on the car at the top of the hill if its speed is $v$?

Accepted Answer

$N = m g - \frac{m v^2}{r}$

Question 11

A block of mass $M$ is attached to a spring and oscillates with amplitude $A$. What is the maximum speed of the block during its motion?

Accepted Answer

$v_{max} = A \sqrt{\frac{k}{M}}$

Question 12

A dart of mass $m$ is shot horizontally into a block of mass $M$ suspended as a pendulum. If the dart sticks to the block, what is the maximum height $h$ the block-dart system will rise after the collision, given the initial speed $v$ of the dart?

Accepted Answer

$h = \frac{(m v)^2}{2 (M + m)^2 g}$

Question 13

A block of mass $m$ slides up a frictional incline of angle $	heta$ and coefficient of kinetic friction $\mu_k$ with initial speed $v_0$. How far $d$ does it travel up the incline before coming to rest?

Accepted Answer

$d = \frac{v_0^2}{2 g (\sin 	heta + \mu_k \cos 	heta)}$

Question 14

The reason an astronaut aboard the International Space Station feels weightless is that:

Accepted Answer

The astronaut is in free fall.

Question 15

A block of mass $m$ moving at speed $v$ compresses a spring by distance $x$. What is the magnitude of the impulse delivered by the spring to the block?

Accepted Answer

$I = m v$

Question 16

A block of mass $m$ is dropped from height $h$ onto a spring with spring constant $k$. What is the maximum compression $x_{max}$ of the spring?

Accepted Answer

$x_{max} = \sqrt{\frac{2 m g h}{k}}$

Question 17

A block of mass $m$ is attached to a spring of constant $k$ and oscillates on a frictionless surface. What is the period $T$ of oscillation?

Accepted Answer

$T = 2 \pi \sqrt{\frac{m}{k}}$

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