Question 1

A cube of uniform metal with edge length $L = 60 \ \mathrm{cm}$ has a hole cut open at the top. Where is the center of mass of the cube located?

Accepted Answer

At $\left( \frac{L}{2}, \frac{L}{2}, \frac{L}{3} \right)$ due to the missing mass at the top

Question 2

A space vehicle is traveling at $4000 \ \mathrm{km/h}$ relative to the Earth when the exhausted rocket motor is disengaged and sent backward at a speed of $80 \ \mathrm{km/h}$$ relative to the command module. If the mass of the command module is $4000 \ \mathrm{kg}$ and the mass of the rocket motor is $1500 \ \mathrm{kg}$, what is the speed of the command module immediately after separation?

Accepted Answer

$4120 \ \mathrm{km/h}$

Question 3

Two blocks, A and B, are held together by a compressed spring between them. When released, the spring pushes them apart. If block A has mass $m_A$ and block B has mass $m_B$, and the spring has stored energy $E$, what is the speed of block A after release?

Accepted Answer

$v_A = \sqrt{\frac{2E m_B}{m_A (m_A + m_B)}}$

Question 4

A $5.0 \ \mathrm{kg}$ block moving at $2.0 \ \mathrm{m/s}$ collides with a $10.0 \ \mathrm{kg}$ block at rest. If the collision is perfectly elastic, what is the velocity of the $5.0 \ \mathrm{kg}$ block after the collision?

Accepted Answer

$0.67 \ \mathrm{m/s}$

Question 5

In a classic elastic collision between a $5.0 \ \mathrm{kg}$ block moving at $2.0 \ \mathrm{m/s}$ and a $10.0 \ \mathrm{kg}$ block at rest, what is the velocity of the $10.0 \ \mathrm{kg}$ block after the collision?

Accepted Answer

$1.33 \ \mathrm{m/s}$

Question 6

A $2.0 \ \mathrm{kg}$ block moving at $3.0 \ \mathrm{m/s}$ on a frictionless surface collides and sticks to a $1.0 \ \mathrm{kg}$ block at rest. What is the final speed of the combined mass?

Accepted Answer

$2.0 \ \mathrm{m/s}$

Question 7

Two $1 \ \mathrm{kg}$ blocks, A and B, collide. The velocities before the collision are $\vec{v}_A = (10\hat{i} + 2\hat{j}) \ \mathrm{m/s}$ and $\vec{v}_B = (-10\hat{i} + 4\hat{j}) \ \mathrm{m/s}$. After the collision, $\vec{v}_A' = (-6.0\hat{i} + 16\hat{j}) \ \mathrm{m/s}$. What is the final velocity of block B?

Accepted Answer

$\vec{v}_B' = (26\hat{i} - 10\hat{j}) \ \mathrm{m/s}$

Question 8

A $78 \ \mathrm{kg}$ man climbs a ladder hanging from a hot air balloon (total mass $320 \ \mathrm{kg}$) at $2.5 \ \mathrm{m/s}$ relative to the ladder. In which direction does the balloon move?

Accepted Answer

Downward

Question 9

A $78 \ \mathrm{kg}$ man climbs a ladder hanging from a hot air balloon (total mass $320 \ \mathrm{kg}$) at $2.5 \ \mathrm{m/s}$ relative to the ladder. What is the speed of the balloon as the man climbs?

Accepted Answer

$0.61 \ \mathrm{m/s}$ downward

Question 10

A car of mass $m$ moves at speed $v$ and is about to jump a gap between a boat and a dock. If the boat and car can be approximated as uniform in their mass distribution, and the boat is initially at rest, what is the width of the gap the car will just be able to make if the car leaves the boat at speed $v$?

Accepted Answer

$d = \frac{v^2}{g}$

Question 11

A $2.0 \ \mathrm{kg}$ block moving at $3.0 \ \mathrm{m/s}$ collides elastically with a $1.0 \ \mathrm{kg}$ block at rest. What is the velocity of the $1.0 \ \mathrm{kg}$ block after the collision?

Accepted Answer

$4.0 \ \mathrm{m/s}$

Question 12

A $2.0 \ \mathrm{kg}$ block moving at $3.0 \ \mathrm{m/s}$ collides elastically with a $1.0 \ \mathrm{kg}$ block at rest. What is the velocity of the $2.0 \ \mathrm{kg}$ block after the collision?

Accepted Answer

$1.0 \ \mathrm{m/s}$

Question 13

A block of mass $m$ is attached to a spring with spring constant $k$ and is compressed a distance $x$ from equilibrium. What is the speed of the block as it passes through equilibrium?

Accepted Answer

$v = \sqrt{\frac{k}{m}} x$

Question 14

A $5.0 \ \mathrm{kg}$ block moving at $2.0 \ \mathrm{m/s}$ collides inelastically with a $10.0 \ \mathrm{kg}$ block at rest. What is the final velocity of the combined mass?

Accepted Answer

$0.67 \ \mathrm{m/s}$

Question 15

A $2.0 \ \mathrm{kg}$ block moving at $3.0 \ \mathrm{m/s}$ collides inelastically with a $1.0 \ \mathrm{kg}$ block at rest. What is the kinetic energy lost in the collision?

Accepted Answer

$2.0 \ \mathrm{J}$

Question 16

A $78 \ \mathrm{kg}$ man climbs a ladder hanging from a hot air balloon (total mass $320 \ \mathrm{kg}$) at $2.5 \ \mathrm{m/s}$ relative to the ladder. If the man stops climbing, what is the speed of the balloon?

Accepted Answer

$0 \ \mathrm{m/s}$

Physics Study Guide: Mechanics and Applications

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