Q: A 2.0 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

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

Q: A 75 kg gymnast jumps vertically upward at $$5.00\ \mathrm{m/s}$$ from a platform $$3.00\ \mathrm{m}$$ above a trampoline. With what speed does he land on the trampoline? ($$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{(5.00)^2$ + 2 \times 9.8 \times 3.00} = 8.37\ \mathrm{m/s}$$

Q: A 2.00 kg cannonball falls vertically downward and hits soft sand at $$25.0\ \mathrm{m/s}$$, penetrating $$2.00\ \mathrm{m}$$ into the sand. What is the average force of friction exerted by the sand?

$$F = \frac{mv^2$}{2d} = \frac{2.00 \times (25.0)^2$}{2 \times 2.00} = 312.5\ \mathrm{N}$$

Q: A 0.65 kg puck is launched up a $$30.0^\circ$$ incline by a spring ($$k = 150\ \mathrm{N/m}) $$compressed $$0.20\ \mathrm{m}. $$The coefficient of kinetic friction is $$0.48. $$The puck slides $$0.25\ \mathrm{m}$$ beyond the relaxed spring. What is the speed as it leaves the ramp? (Neglect air resistance.)

Use $$\frac{1}{2}kx^2$ = \frac{1}{2}mv^2$ + mgd\sin\theta + f_k d$$; $$v = 1.7\ \mathrm{m/s}$$

Question 1

A 2.0 kg object is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before it hits the ground? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

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

Question 2

A block of mass $$m$$ slides down a frictionless ramp from rest and reaches speed $$v at $$the bottom. To reach speed $$2v at $$the bottom, how many times higher must the ramp be?

Accepted Answer

4 times as high

Question 3

A spring with spring constant $$k is $$compressed by a distance $$x$$ and launches a puck across a frictionless surface with speed $$v. If $$the spring is compressed by $$3x$$, what is the new launch speed?

Accepted Answer

$$v_{new} = v \sqrt{3}$$

Question 4

A 75 kg gymnast jumps vertically upward at $$5.00\ \mathrm{m/s}$$ from a platform $$3.00\ \mathrm{m}$$ above a trampoline. With what speed does he land on the trampoline? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{(5.00)^2$ + 2 	imes 9.8 	imes 3.00} = 8.37\ \mathrm{m/s}$$

Question 5

Which of the following statements about conservative forces is TRUE?

Accepted Answer

The work done by a conservative force is independent of the path taken.

Question 6

A 2.00 kg cannonball falls vertically downward and hits soft sand at $$25.0\ \mathrm{m/s}$$, penetrating $$2.00\ \mathrm{m}$$ into the sand. What is the average force of friction exerted by the sand?

Accepted Answer

$$F = \frac{mv^2$}{2d} = \frac{2.00 	imes (25.0)^2$}{2 	imes 2.00} = 312.5\ \mathrm{N}$$

Question 7

A mass $$m$$ oscillates on a spring with total mechanical energy $$E_{mech}. At $$the turning points of the motion, which of the following is true?

Accepted Answer

Kinetic energy is zero and potential energy equals total energy.

Question 8

A particle moves along the $$y-$$axis with potential energy $$U = \frac{2}{y^3$} J$$, where $$y is in $$meters. What is the $$y-$$component of the force at $$y = 2.0\ \mathrm{m}$$?

Accepted Answer

$$F_y = -\frac{dU}{dy} = -\frac{2}{2.0^4$} = -0.125\ \mathrm{N}$$

Question 9

Which of the following best describes the energy transformation when a block slides down a rough incline and compresses a spring at the bottom?

Accepted Answer

Gravitational potential energy is converted into kinetic energy, elastic potential energy, and thermal energy.

Question 10

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and is displaced by $$x$$ from equilibrium. What is the elastic potential energy stored in the spring?

Accepted Answer

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

Question 11

A 0.65 kg puck is launched up a $$30.0^\circ$$ incline by a spring ($$k = 150\ \mathrm{N/m}) $$compressed $$0.20\ \mathrm{m}. $$The coefficient of kinetic friction is $$0.48. $$The puck slides $$0.25\ \mathrm{m}$$ beyond the relaxed spring. What is the speed as it leaves the ramp? (Neglect air resistance.)

Accepted Answer

Use $$\frac{1}{2}kx^2$ = \frac{1}{2}mv^2$ + mgd\sin	heta + f_k d$$; $$v = 1.7\ \mathrm{m/s}$$

Question 12

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

Accepted Answer

The work done depends on the path taken.

Question 13

A 10 g particle is released from rest at $$x = 4\ \mathrm{m} on a $$potential energy curve. What is the direction of the initial force acting on the particle?

Accepted Answer

Toward decreasing $$x ($$leftward), since force is $$F = -\frac{dU}{dx}$$ and $$U$$ increases with $$x at$$ $$x=4.$$

Question 14

A block of mass $$m is $$released from rest at height $$h$$ above the ground. If the reference point for gravitational potential energy is changed from the ground to height $$h$$, what happens to the value of $$U_g at $$the starting point?

Accepted Answer

$$U_g$$ becomes zero at the starting point.

Question 15

A spring is stretched by $$0.10\ \mathrm{m}$$ from equilibrium. If the spring constant is $$120\ \mathrm{N/m}$$, what is the magnitude of the restoring force?

Accepted Answer

$$F = kx = 120 	imes 0.10 = 12\ \mathrm{N}$$

Question 16

A 2.0 kg block slides $$5.0\ \mathrm{m}$$ across a rough surface with kinetic friction force $$f_k = 10\ \mathrm{N}. $$How much thermal energy is generated?

Accepted Answer

$$\Delta E_{th} = f_k \Delta s = 10 	imes 5.0 = 50\ \mathrm{J}$$

Question 17

Which of the following best describes the relationship between kinetic energy and speed?

Accepted Answer

Kinetic energy is proportional to the square of the speed: $$K = \frac{1}{2}mv^2$

Question 18

A ball is thrown vertically upward with speed $$v_0$$ from ground level. At its maximum height, what is its kinetic energy?

Accepted Answer

Zero, since all energy is potential at the top.

Chapter 10: Energy – Kinetic, Potential, and Conservation Principles

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