Q: A 0.33 kg volleyball is thrown vertically downward with a speed of 0.150 m/s from a height where $$g = 9.81\ \mathrm{m/s^2$}. If it $$takes 0.0655 s to reach the ground, what is the magnitude of its momentum just before it hits the ground?

$$p = m(v_0$ + g t) = 0.33\ \mathrm{kg} (0.150 + 9.81 \times 0.0655) = 0.33 \times 0.792 = 0.262\ \mathrm{kg\cdot m/s}$$

Q: A 1000 kg whale swims horizontally at 6.0 m/s and collides with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds on. What is their speed immediately after the collision? (Neglect drag and external forces.)

$$v = \frac{m_1$ v_1$}{m_1$ + m_2$} = \frac{1000 \times 6.0}{1000 + 200} = 5.0\ \mathrm{m/s}$$

Q: A 0.140 kg baseball is thrown with a velocity of 27.0 m/s. It is struck by a bat with an average force of 5000 N, resulting in a velocity of 37.0 m/s in the opposite direction. How long were the ball and bat in contact?

$$\Delta t = \frac{m(v_f - v_i)}{F} = \frac{0.140 \times ( -37.0 - 27.0 )}{5000} = \frac{0.140 \times ( -64.0 )}{5000} = 1.79 \times 10$$^{-3}$$\ \mathrm{s}$$

Q: A 600 kg car makes a 90° turn. Its speed before the turn is 21.0 m/s and after the turn is 24.0 m/s. What is the magnitude of the change in the car's momentum during the turn?

$$\Delta p = m \sqrt{v_1$^2 + v_2$^2} = 600 \times \sqrt{21.0^2$ + 24.0^2$} = 600 \times 31.89 = 19,134\ \mathrm{kg\cdot m/s}$$

Q: A 5.0 kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 225 N force will make the child lift off the ground?

$$d = \frac{m g \times 1.5}{225} = \frac{5.0 \times 9.81 \times 1.5}{225} = 0.327\ \mathrm{m}$$

Q: A 1.50-m-long, 300-kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. The gravitational torque about the point where the beam is bolted into place is 3,250 N·m. How heavy, in kilograms, is a construction worker standing at the end of the beam away from the building?

$$\tau = m g d \implies m = \frac{3250}{9.81 \times 1.0} = 331\ \mathrm{kg}$$

Question 1

A 12.0 kg box is dragged 5.00 meters across a carpet at a constant velocity by a force of 40.0 N applied at an angle of 30.0° above the horizontal. If the coefficient of friction between the box and the carpet is 0.300, how much work is done by friction during the displacement?

Accepted Answer

$$W_\mathrm{fric} = -\mu_k m g d = -(0.300)(12.0\ \mathrm{kg})(9.81\ \mathrm{m/s^2$})(5.00\ \mathrm{m}) = -176\ \mathrm{J}$$

Question 2

A 60.0 kg skier starts from rest at the top of a 300 m high hill and skis down to the bottom, reaching a speed of 25.0 m/s. How much energy was lost to friction during the descent? (Assume $$g = 9.81\ \mathrm{m/s^2$})$$

Accepted Answer

$$E_\mathrm{fric} = mgh - \frac{1}{2}mv^2$ = (60.0)(9.81)(300) - 0.5(60.0)(25.0^2$) = 176,580 - 18,750 = 157,830\ \mathrm{J}$$

Question 3

A 0.33 kg volleyball is thrown vertically downward with a speed of 0.150 m/s from a height where $$g = 9.81\ \mathrm{m/s^2$}. If it $$takes 0.0655 s to reach the ground, what is the magnitude of its momentum just before it hits the ground?

Accepted Answer

$$p = m(v_0$ + g t) = 0.33\ \mathrm{kg} (0.150 + 9.81 	imes 0.0655) = 0.33 	imes 0.792 = 0.262\ \mathrm{kg\cdot m/s}$$

Question 4

A 1000 kg whale swims horizontally at 6.0 m/s and collides with a stationary seal of mass 200 kg. The seal grabs onto the whale and holds on. What is their speed immediately after the collision? (Neglect drag and external forces.)

Accepted Answer

$$v = \frac{m_1$ v_1$}{m_1$ + m_2$} = \frac{1000 	imes 6.0}{1000 + 200} = 5.0\ \mathrm{m/s}$$

Question 5

A 0.140 kg baseball is thrown with a velocity of 27.0 m/s. It is struck by a bat with an average force of 5000 N, resulting in a velocity of 37.0 m/s in the opposite direction. How long were the ball and bat in contact?

Accepted Answer

$$\Delta t = \frac{m(v_f - v_i)}{F} = \frac{0.140 	imes ( -37.0 - 27.0 )}{5000} = \frac{0.140 	imes ( -64.0 )}{5000} = 1.79 	imes 10$$^{-3}$$\ \mathrm{s}$$

Question 6

A 600 kg car makes a 90° turn. Its speed before the turn is 21.0 m/s and after the turn is 24.0 m/s. What is the magnitude of the change in the car's momentum during the turn?

Accepted Answer

$$\Delta p = m \sqrt{v_1$^2 + v_2$^2} = 600 	imes \sqrt{21.0^2$ + 24.0^2$} = 600 	imes 31.89 = 19,134\ \mathrm{kg\cdot m/s}$$

Question 7

A 5.0 kg child is sitting on a playground teeter-totter, 1.5 m from the pivot. What is the minimum distance, on the other side of the pivot, such that a 225 N force will make the child lift off the ground?

Accepted Answer

$$d = \frac{m g 	imes 1.5}{225} = \frac{5.0 	imes 9.81 	imes 1.5}{225} = 0.327\ \mathrm{m}$$

Question 8

A 2.0 kg object at rest explodes into two fragments of masses 0.7 kg and 1.3 kg that move in opposite directions. If the explosion creates 1,000 J of thermal energy and the first object is expelled at 11.5 m/s, what is the total internal energy of the explosion?

Accepted Answer

$$E_\mathrm{int} = \frac{1}{2} m_1$ v_1$^2 + \frac{1}{2} m_2$ v_2$^2 + 1000 = 3757\ \mathrm{J}$$

Question 9

In a certain nuclear reaction, neutrons suddenly collide with carbon nuclei, which have 12 times the mass of neutrons, in a head-on elastic collision with a stationary carbon nucleus. What fraction of the neutron's initial speed does the carbon nucleus have after the collision?

Accepted Answer

$$\frac{2}{13}$$

Question 10

A 1.50-m-long, 300-kg steel beam extends horizontally from the point where it has been bolted to the framework of a new building under construction. The gravitational torque about the point where the beam is bolted into place is 3,250 N·m. How heavy, in kilograms, is a construction worker standing at the end of the beam away from the building?

Accepted Answer

$$	au = m g d \implies m = \frac{3250}{9.81 	imes 1.0} = 331\ \mathrm{kg}$$

Question 11

If the sum of the external forces on an object is zero, then the sum of the external torques on it must also be zero.

Accepted Answer

False

Question 12

A block of mass 34 kg and speed 0.90 m/s behind a block of mass 81 kg and speed 0.50 m/s. The surface is frictionless and the blocks collide and stick together. What is the magnitude of the impulse on the 34-kg block due to the collision?

Accepted Answer

$$J = m_1$ (v_f - v_{i1}) = 34 (0.90 - 0.50) = 13.6\ \mathrm{kg\cdot m/s}$$

Question 13

A 0.051 kg steel ball is released from rest and falls vertically onto a steel plate. The ball bounces elastically and returns to its original height. If the contact time with the plate is 0.0050 s, what is the magnitude of the average force exerted on the ball by the plate during contact?

Accepted Answer

$$F_{avg} = \frac{\Delta p}{\Delta t} = \frac{1.499}{0.0050} = 2.998\ \mathrm{N}$$

Question 14

A 500 kg rollercoaster car is traveling at 15.0 m/s as it crests a peak 50.0 m above the ground. Before it reaches the next peak, which is 30.0 m above the ground, it will need to travel over another 200 m of track. Assuming the motion of the car is resisted by an average frictional force of 740 N along this length of track, what is the minimum amount of energy that must be exerted on the cart to ensure that it clears the next peak?

Accepted Answer

$$E = m g (h_1$ - h_2$) + \frac{1}{2} m (v_1$^2 - v_2$^2) + F_{fric} d = 500 	imes 9.81 	imes (50 - 30) + 0.5 	imes 500 	imes (15^2$ - 0) + 740 	imes 200 = 98,100 + 56,250 + 148,000 = 302,350\ \mathrm{J}$$

Question 15

A store's sign has a mass of 20 kg and is 2.0 m long. Its center of gravity is at the center of the sign. It is supported horizontally by a small hinge bolt attached to the wall at one end and by a wire at the other end, as shown in the figure. What is the tension in the wire? (Assume the wire makes a 25° angle with the horizontal.)

Accepted Answer

$$T = \frac{mg r_{cg}}{r_w \sin 25^\circ} = \frac{20 	imes 9.81 	imes 1.0}{2.0 	imes \sin 25^\circ} = 230\ \mathrm{N}$$

Question 16

A golf club exerts an average horizontal force of 1000 N on a 0.045-kg golf ball that is initially at rest on the tee. The club is in contact with the ball for 0.018 s. What is the speed of the golf ball just as it leaves the tee?

Accepted Answer

$$v = \frac{F_{avg} \Delta t}{m} = \frac{1000 	imes 0.018}{0.045} = 40\ \mathrm{m/s}$$

Question 17

A 7.5-kg shotput is held in the hand with the lower arm horizontal. The lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint. The shot is 35 cm from the elbow. How much force must the extensor muscle (which is 3.0 cm from the elbow) exert to hold the shot steady?

Accepted Answer

$$F_m = \frac{m_{shot} g r_{shot} + m_{forearm} g r_{forearm}}{r_m} = \frac{7.5 	imes 9.81 	imes 0.35 + 2.8 	imes 9.81 	imes 0.12}{0.03} = 1,000\ \mathrm{N}$$

Question 18

If an object remains at rest, then the sum of both the external torques and the external forces on the object must be zero.

Accepted Answer

True

Physics Study Guide: Conservation of Energy, Linear Momentum, and Torque

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