Q: A 24500 kg jet lands on an aircraft carrier and is brought to rest from 65 m/s over a distance of 96 m by a cable. What is the average force exerted by the cable on the jet? (Ignore friction and air resistance.)

$F = m a = 24500 \times \frac{65^2}{2 \times 96} = 538,151\ \mathrm{N}$

Q: A 5 kg object is dropped from a height of 10 m. What is its speed just before hitting the ground? (Ignore air resistance.)

$v = \sqrt{2 g h} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$

Q: A car of mass 1000 kg is moving at 20 m/s. What is its kinetic energy?

$K = \frac{1}{2} m v^2 = \frac{1}{2} \times 1000 \times 20^2 = 200,000\ \mathrm{J}$

Q: A 1 kg object is thrown vertically upward with a speed of 10 m/s. What is the maximum height it reaches? (Ignore air resistance.)

$h = \frac{v^2}{2g} = \frac{10^2}{2 \times 9.8} = 5.1\ \mathrm{m}$

Question 1

A 24500 kg jet lands on an aircraft carrier and is brought to rest from 65 m/s over a distance of 96 m by a cable. What is the average force exerted by the cable on the jet? (Ignore friction and air resistance.)

Accepted Answer

$F = m a = 24500 	imes \frac{65^2}{2 	imes 96} = 538,151\ \mathrm{N}$

Question 2

Which of the following statements about conservative forces is correct?

Accepted Answer

The work done by a conservative force over a closed path is zero.

Question 3

A block of mass $m$ slides down a frictionless incline of height $h$. What is its speed at the bottom?

Accepted Answer

$v = \sqrt{2 g h}$

Question 4

Which equation correctly expresses the work-energy theorem?

Accepted Answer

$W_{tot} = K_2 - K_1 = \Delta K$

Question 5

A spring with spring constant $k$ is compressed by a distance $x$. What is the elastic potential energy stored in the spring?

Accepted Answer

$U_{el} = \frac{1}{2} k x^2$

Question 6

A 10 kg block slides down a frictionless track and compresses a spring with $k = 800\ \mathrm{N/m}$ by $0.1$ m. What is the speed of the block just before it contacts the spring?

Question 7

Which of the following is NOT a property of a non-conservative force?

Accepted Answer

The work done by the force over a closed path is zero.

Question 8

A 20 kg block (A) is connected by a rope over a frictionless pulley to a 10 kg block (B) hanging vertically. The coefficient of kinetic friction between block A and the inclined plane is $\mu_k = 0.20$. If block A slides 2 m down the incline from rest, what is the work done by friction?

Accepted Answer

$W_{fric} = -\mu_k m_A g d$

Question 9

Which of the following correctly expresses the gravitational potential energy of a mass $m$ at height $y$ above Earth's surface?

Accepted Answer

$U_{grav} = m g y$

Question 10

A satellite of mass $m$ orbits Earth at a distance $r$ from the center. What is the gravitational potential energy of the satellite-Earth system?

Accepted Answer

$U_{grav} = -\frac{G M m}{r}$

Question 11

Which of the following best describes the relationship between force and potential energy for a conservative force in one dimension?

Accepted Answer

$F(x) = -\frac{dU}{dx}$

Question 12

A 5 kg object is dropped from a height of 10 m. What is its speed just before hitting the ground? (Ignore air resistance.)

Accepted Answer

$v = \sqrt{2 g h} = \sqrt{2 	imes 9.8 	imes 10} = 14\ \mathrm{m/s}$

Question 13

Which of the following is a correct statement of the law of conservation of mechanical energy for an isolated system with only conservative forces?

Accepted Answer

$K_1 + U_1 = K_2 + U_2$

Question 14

A 2 kg mass is attached to a spring with $k = 200\ \mathrm{N/m}$ and is compressed by 0.1 m. What is the maximum speed the mass will reach when released from rest?

Question 15

Which of the following is true about the work done by gravity when an object moves from height $y_1$ to $y_2$?

Accepted Answer

$W_{grav} = -m g (y_2 - y_1)$

Question 16

A car of mass 1000 kg is moving at 20 m/s. What is its kinetic energy?

Accepted Answer

$K = \frac{1}{2} m v^2 = \frac{1}{2} 	imes 1000 	imes 20^2 = 200,000\ \mathrm{J}$

Question 17

Which of the following is a correct expression for instantaneous power delivered by a force $\vec{F}$ acting on a particle with velocity $\vec{v}$?

Accepted Answer

$P = \vec{F} \cdot \vec{v}$

Question 18

A 1 kg object is thrown vertically upward with a speed of 10 m/s. What is the maximum height it reaches? (Ignore air resistance.)

Accepted Answer

$h = \frac{v^2}{2g} = \frac{10^2}{2 	imes 9.8} = 5.1\ \mathrm{m}$

Question 19

Which of the following is the correct expression for the escape velocity from the surface of a planet of mass $M$ and radius $R$?

Accepted Answer

$v_{esc} = \sqrt{\frac{2 G M}{R}}$

H6-7

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