Q: A $4000\,\mathrm{kg}$ truck moving at $25\,\mathrm{m/s}$ comes to rest in a sandy patch. How much work is required to stop the truck?

$W = -\frac{1}{2}mv^2 = -\frac{1}{2}(4000)(25^2) = -1.25 \times 10^6\,\mathrm{J}$

Question 1

A 20 kg box is pulled across a rough floor ($\mu = 0.4$) using a rope at $45^\circ$ above the horizontal. The box moves at a constant velocity for 10 meters. What is the work done by the friction force?

Accepted Answer

$W = (56\,\mathrm{N})(10\,\mathrm{m}) = 560\,\mathrm{J}$

Question 2

Which equation correctly expresses the work done by a constant force $F$ acting at an angle $	heta$ to the direction of displacement $d$?

Accepted Answer

$W = Fd\cos	heta$

Question 3

A runaway truck ($m = 4000\,\mathrm{kg}$) moving at $25\,\mathrm{m/s}$ enters a sandy patch and comes to rest after $100\,\mathrm{m}$. What is the magnitude of the friction force required to stop the truck?

Accepted Answer

$F = -12,500\,\mathrm{N}$

Question 4

Which of the following best describes kinetic energy?

Accepted Answer

Energy of motion, given by $KE = \frac{1}{2}mv^2$

Question 5

A perfectly elastic spring requires $0.54\,\mathrm{J}$ of work to stretch $6\,\mathrm{cm}$ from equilibrium. What is the spring constant $k$?

Accepted Answer

$k = 300\,\mathrm{N/m}$

Question 6

A cart of mass $500\,\mathrm{kg}$ moves through a carnival ride with several hills. If the cart is at a height of $40\,\mathrm{m}$, what is its gravitational potential energy?

Accepted Answer

$PE = (500)(9.8)(40) = 196,000\,\mathrm{J}$

Question 7

Which of the following is the correct expression for the work-energy principle?

Accepted Answer

$W_{net} = \Delta KE = \frac{1}{2}mv^2 - \frac{1}{2}mv_0^2$

Question 8

If a force $F(x)$ varies with position, which integral gives the total work done from $x_1$ to $x_2$?

Accepted Answer

$W = \int_{x_1}^{x_2} F(x)\,dx$

Question 9

A spring is stretched $12\,\mathrm{cm}$ from equilibrium. If $k = 300\,\mathrm{N/m}$, how much work is required?

Accepted Answer

$W = \frac{1}{2}kx^2 = \frac{1}{2}(300)(0.12^2) = 2.16\,\mathrm{J}$

Question 10

A person lifts a $20\,\mathrm{kg}$ box vertically upward $2\,\mathrm{m}$ at constant velocity. What is the work done by the applied force?

Accepted Answer

$W = mgh = (20)(9.8)(2) = 392\,\mathrm{J}$

Question 11

Which of the following is NOT a form of potential energy discussed in the lecture?

Accepted Answer

Thermal potential energy

Question 12

A $2\,\mathrm{kg}$ object accelerates from $5\,\mathrm{m/s}$ to $15\,\mathrm{m/s}$. What is the change in kinetic energy?

Accepted Answer

$\Delta KE = \frac{1}{2}m(v^2 - v_0^2) = \frac{1}{2}(2)(225 - 25) = 200\,\mathrm{J}$

Question 13

Which statement about the work done by the normal force on a box sliding horizontally is correct?

Accepted Answer

The work done by the normal force is zero because the force is perpendicular to the displacement.

Question 14

A $4000\,\mathrm{kg}$ truck moving at $25\,\mathrm{m/s}$ comes to rest in a sandy patch. How much work is required to stop the truck?

Accepted Answer

$W = -\frac{1}{2}mv^2 = -\frac{1}{2}(4000)(25^2) = -1.25 	imes 10^6\,\mathrm{J}$

Question 15

Which formula gives the elastic potential energy stored in a spring stretched a distance $x$?

Accepted Answer

$PE = \frac{1}{2}kx^2$

Question 16

A $500\,\mathrm{kg}$ cart at $10\,\mathrm{m}$ height has $PE = 49,000\,\mathrm{J}$. If it descends to $2\,\mathrm{m}$, what is the change in gravitational potential energy?

Accepted Answer

$\Delta PE = (500)(9.8)(2 - 10) = -39,200\,\mathrm{J}$

Question 17

Which of the following is true about the sign of work done by friction?

Accepted Answer

Work done by friction is negative because it acts opposite to the direction of motion.

Question 18

A $1\,\mathrm{kg}$ object is dropped from a height of $10\,\mathrm{m}$. What is its velocity just before hitting the ground, assuming no air resistance?

Accepted Answer

$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} \approx 14\,\mathrm{m/s}$

Energy & Work: Fundamental Concepts in Physics

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