Q: A freight train has a mass of $$1.5 \times 10^7$\ \mathrm{kg}. If $$the locomotive can exert a constant pull of $$7.5 \times 10^5$\ \mathrm{N}$$, how long does it take to increase the speed of the train from rest to $$80\ \mathrm{km/h}$$?

$$t = \dfrac{m(v - v_0$)}{F} = \dfrac{1.5 \times 10^7$\ \mathrm{kg} \times (22.2\ \mathrm{m/s})}{7.5 \times 10^5$\ \mathrm{N}} = 444\ \mathrm{s}$$

Q: A block of mass $$2.50\ \mathrm{kg} is $$pushed $$2.20\ \mathrm{m}$$ along a frictionless horizontal table by a constant applied force of $$150\ \mathrm{N}$$ directed at an angle of $$25.0^\circ$$ below the horizontal. What is the work done by the applied force?

$$W = Fd \cos \theta = 150 \times 2.20 \times \cos 25^\circ = 299\ \mathrm{J}$$

Q: A 65.0-kg runner has a speed of $$5.20\ \mathrm{m/s} at $$one instant. What is his kinetic energy at this instant?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 65.0 \times (5.20)^2$ = 878\ \mathrm{J}$$

Q: A 7.80-g bullet moving at $$575\ \mathrm{m/s}$$ penetrates a tree trunk to a depth of $$5.50\ \mathrm{cm}. $$What is the average frictional force that stops the bullet?

$$F = \frac{mv^2$}{2d} = \frac{0.0078 \times (575)^2$}{2 \times 0.055} = 2,930\ \mathrm{N}$$

Q: A 2.50-kg object is hung vertically on a spring and stretches it $$2.76\ \mathrm{cm}. $$What is the force constant $$k of $$the spring?

$$k = \frac{mg}{\Delta x} = \frac{2.50 \times 9.8}{0.0276} = 888\ \mathrm{N/m}$$

Q: A skier of mass $$70\ \mathrm{kg} is $$pulled up a $$34^\circ$$ slope by a motor-driven cable at a constant speed of $$2.0\ \mathrm{m/s}. $$How much work is required to pull him $$60\ \mathrm{m} up $$the slope (assume frictionless)?

$$W = mgd \sin \theta = 70 \times 9.8 \times 60 \times \sin 34^\circ = 23,100\ \mathrm{J}$$

Question 1

A 75-kg man stands on a scale in an elevator. As the elevator rises, the scale reads 825 N. What is the acceleration of the elevator?

Accepted Answer

$$a = \dfrac{825\ \mathrm{N} - (75\ \mathrm{kg})(9.8\ \mathrm{m/s}^2)}{75\ \mathrm{kg}} = 1.2\ \mathrm{m/s}^2$$

Question 2

A freight train has a mass of $$1.5 	imes 10^7$\ \mathrm{kg}. If $$the locomotive can exert a constant pull of $$7.5 	imes 10^5$\ \mathrm{N}$$, how long does it take to increase the speed of the train from rest to $$80\ \mathrm{km/h}$$?

Accepted Answer

$$t = \dfrac{m(v - v_0$)}{F} = \dfrac{1.5 	imes 10^7$\ \mathrm{kg} 	imes (22.2\ \mathrm{m/s})}{7.5 	imes 10^5$\ \mathrm{N}} = 444\ \mathrm{s}$$

Question 3

A 0.50-kg ball falls from rest from a height of $$30\ \mathrm{m}$$ and rebounds upward, reaching a height of $$20\ \mathrm{m}. If $$the contact between ball and ground lasted $$2.0\ \mathrm{ms}$$, what average force was exerted on the ball?

Accepted Answer

$$F_{\mathrm{avg}} = \dfrac{\Delta p}{\Delta t} = \dfrac{m(v_{\mathrm{up}} + v_{\mathrm{down}})}{\Delta t} = \dfrac{0.5 	imes (19.8 + 24.3)}{0.002} = 11,025\ \mathrm{N}$$

Question 4

A sailboat experiences a $$390\ \mathrm{N}$$ force north from the wind and a $$180\ \mathrm{N}$$ force east from the water. If the boat's mass is $$270\ \mathrm{kg}$$, what is the magnitude of its acceleration?

Accepted Answer

$$a = \dfrac{\sqrt{390^2$ + 180^2$}}{270} = 1.6\ \mathrm{m/s}^2$$

Question 5

Which of the following best describes Newton's Third Law?

Accepted Answer

For every action, there is an equal and opposite reaction: $$\vec{F}_{12} = -\vec{F}_{21}$$

Question 6

A block of mass $$2.50\ \mathrm{kg} is $$pushed $$2.20\ \mathrm{m}$$ along a frictionless horizontal table by a constant applied force of $$150\ \mathrm{N}$$ directed at an angle of $$25.0^\circ$$ below the horizontal. What is the work done by the applied force?

Accepted Answer

$$W = Fd \cos 	heta = 150 	imes 2.20 	imes \cos 25^\circ = 299\ \mathrm{J}$$

Question 7

A 65.0-kg runner has a speed of $$5.20\ \mathrm{m/s} at $$one instant. What is his kinetic energy at this instant?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 65.0 	imes (5.20)^2$ = 878\ \mathrm{J}$$

Question 8

A 7.80-g bullet moving at $$575\ \mathrm{m/s}$$ penetrates a tree trunk to a depth of $$5.50\ \mathrm{cm}. $$What is the average frictional force that stops the bullet?

Accepted Answer

$$F = \frac{mv^2$}{2d} = \frac{0.0078 	imes (575)^2$}{2 	imes 0.055} = 2,930\ \mathrm{N}$$

Question 9

A 2.50-kg object is hung vertically on a spring and stretches it $$2.76\ \mathrm{cm}. $$What is the force constant $$k of $$the spring?

Accepted Answer

$$k = \frac{mg}{\Delta x} = \frac{2.50 	imes 9.8}{0.0276} = 888\ \mathrm{N/m}$$

Question 10

A skier of mass $$70\ \mathrm{kg} is $$pulled up a $$34^\circ$$ slope by a motor-driven cable at a constant speed of $$2.0\ \mathrm{m/s}. $$How much work is required to pull him $$60\ \mathrm{m} up $$the slope (assume frictionless)?

Accepted Answer

$$W = mgd \sin 	heta = 70 	imes 9.8 	imes 60 	imes \sin 34^\circ = 23,100\ \mathrm{J}$$

Question 11

A 0.290-kg volleyball approaches a player horizontally at $$13.0\ \mathrm{m/s}. $$The player strikes the ball so it moves in the opposite direction at $$22.0\ \mathrm{m/s}. $$What impulse is delivered to the ball by the player?

Accepted Answer

$$J = m(v_f - v_i) = 0.290 	imes (-22.0 - 13.0) = -10.2\ \mathrm{kg\cdot m/s}$$

Question 12

Drops of rain fall vertically onto a car roof at $$12\ \mathrm{m/s}$$, with a mass rate of $$0.035\ \mathrm{kg/s}. $$What is the average force exerted by the rain on the roof?

Accepted Answer

$$F = \Delta p / \Delta t = (0.035)(12) = 0.42\ \mathrm{N}$$

Question 13

A dentist's drill starts from rest. After $$3.20\ \mathrm{s} of $$constant angular acceleration, it turns at a rate of $$2.51 	imes 10^4$\ \mathrm{rev/min}. $$What is the angular acceleration in $$\mathrm{rad/s}^2$$?

Accepted Answer

$$\alpha = \dfrac{\omega_f - \omega_i}{t} = \dfrac{2.51 	imes 10^4$ 	imes 2\pi / 60}{3.20} = 82.2\ \mathrm{rad/s}^2$$

Question 14

Which equation correctly expresses the work-energy theorem?

Accepted Answer

$$W_{\mathrm{net}} = \Delta KE$$

Question 15

A block of mass $$m$$ slides down a frictionless track from a height $$h_A = 5.00\ \mathrm{m} to$$ $$h_C = 2.00\ \mathrm{m}. $$What is its speed at point C?

Accepted Answer

$$v_C = \sqrt{2g(h_A - h_C)} = \sqrt{2 	imes 9.8 	imes (5.00 - 2.00)} = 7.67\ \mathrm{m/s}$$

Question 16

A rotating wheel requires $$5.00\ \mathrm{s} to $$rotate $$57.0$$ revolutions. Its angular velocity at the end of the interval is $$98.0\ \mathrm{rad/s}. $$What is the constant angular acceleration?

Accepted Answer

$$\alpha = \dfrac{\omega_f - \omega_i}{t} = \dfrac{98.0 - 0}{5.00} = 19.6\ \mathrm{rad/s}^2$$

Question 17

A 12.0-g bullet is fired horizontally into a 100-g wooden block attached to a spring ($$k = 150\ \mathrm{N/m}). If $$the spring compresses by $$80.0\ \mathrm{cm}$$, what was the speed of the bullet at impact?

Accepted Answer

$$v = \sqrt{\dfrac{kx^2$}{m}} = \sqrt{\dfrac{150 	imes (0.80)^2$}{0.112}} = 28.7\ \mathrm{m/s}$$

Fundamental Principles of Motion, Energy, and Momentum in Physics

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