Chapter 2 Exercises
26. You can say that no net force acts on a body at rest, but there may be any number of forces that act to produce a zero net force. When the net force is zero, the body is in static equilibrium.
38. Friction on the cart has to be 200 N, opposite to your 200-N pull.
Chapter 2 Problems
4. From the equilibrium rule, SF = 0, the upward forces are 800 N + tension in the right scale. This sum must equal the downward forces 500 N + 400 N + 400 N. Arithmetic shows the reading on the right scale is 500 N.
Chapter 3 Ranking
4. a. C, B, A
b. A = B = C (10 m/s2)
Chapter 3 Exercises
4. The speeds of both are exactly the same, but the velocities are not. Velocity includes direction, and since the directions of the airplanes are opposite, their velocities are opposite. The velocities would be equal only if both speed and direction were the same.
16. An object moving in a circular path at constant speed is a simple example of acceleration at constant speed because its velocity is changing direction. No example can be given for the second case, for constant velocity means zero acceleration. You can’t have a nonzero acceleration while having a constant velocity. There are no examples of things that accelerate while not accelerating.
22. The greater change in speeds occurs for (30 km/h – 25 km/h = 5 km/h) which is greater than (100 km/h – 96 km/h = 4 km/h). So for the same time, the slower one has the greater acceleration.
Chapter 4 Ranking
2. C, B, A
4. a. C, A, B
b. B, A, C
Chapter 4 Exercises
14. Ten kilograms weighs about 100 N on the Earth (weight = mg = 10 kg ´ 10 m/s2 = 100 N or 98 N if g = 9.8 m/s2 is used). On the Moon, weight would be 1⁄6 of 100 N = 16.7 N (or 16.3 N if g = 9.8 m/s2 is used). The mass would be 10 kg everywhere.
22. Agree. Acceleration (slowing the car) is opposite to velocity (the direction the car is moving).
38. When held at rest the upward support force equals the gravitational force on the apple and the net force is zero. When released, the upward support force is no longer there and the net force is the gravitational force, 1 N. (If the apple falls fast enough for air resistance to be important, then the net force will be less than 1 N, and eventually can reach zero if air resistance builds up to 1 N.)
Chapter 5 Exercises
4. (a) Action; hammer hits nail. Reaction; nail hits hammer.
(b) Action; Earth pulls down on a book. Reaction; book pulls up on Earth.
(c) Action; helicopter blade pushes air downward. Reaction; air pushes helicopter blade upward. (In these examples, action and reaction may be reversed—which is called which is unimportant.)
24. In accord with Newton’s 3rd law, the force on each will be of the same magnitude. But the effect of the force (acceleration) will be different for each because of the different mass. The more massive truck undergoes less change in motion than the Civic.
Chapter 6 Ranking
4. C, A, B
Chapter 6 Exercises
6. The steel cord will stretch only a little, resulting in a short time of stop and a correspondingly large force. Ouch!
16. No. The gun would recoil with a speed ten times the muzzle velocity. Firing such a gun in the conventional way would not be a good idea!
46. By Newton’s 3rd law, the force on the bug is equal in magnitude and opposite in direction to the force on the car windshield. The rest is logic: Since the time of impact is the same for both, the amount of impulse is the same for both, which means they both undergo the same change in momentum. The change in momentum of the bug is evident because of its large change in speed. The same change in momentum of the considerably more massive car is not evident, for the change in speed is correspondingly very small. Nevertheless, the magnitude of m∆V for the bug is equal to M∆v for the car!
Chapter 7 Exercises
6. Work done by each is the same, for they reach the same height. The one who climbs in 30 s uses more power because work is done in a shorter time.
Chapter 8 Ranking
4. B, C, A
Chapter 8 Exercises
18. The lever arm is the same whether a person stands, sits, or hangs from the end of the seesaw, and certainly the person’s weight is the same. So the net torque is the same also.
Chapter 9 Exercises
14. The Earth and Moon equally pull on each other in a single interaction. In accord with Newton’s 3rd law, the pull of the Earth on the Moon is equal and opposite to the pull of the Moon on the Earth. An elastic band pulls equally on the fingers that stretch it.
18. Letting the equation for gravitation guide your thinking, twice the mass means twice the force, and twice the distance means one-quarter the force. Combined, the astronaut weighs half as much.
Chapter 10 Ranking
2. a. A = B = C
b. A = B = C
c. A = B = C
d. B, A, C
4. a. A, B, C, D
b. A, B, C, D
c. A, B, C, D
d. A, B, C, D
e. D, C, B, A
f. A = B = C = D
g. A, B, C, D
Chapter 10 Exercises
2. In accord with the principle of horizontal and vertical projectile motion, the time to hit the floor is independent of the ball’s speed.
8. There are no forces horizontally (neglecting air drag) so there is no horizontal acceleration, hence the horizontal component of velocity doesn’t change. Gravitation acts vertically, which is why the vertical component of velocity changes.
58. The satellite experiences the greatest gravitational force at A, where it is closest to the Earth, the perigee; and the greatest speed and the greatest velocity at A, and by the same token the greatest momentum and greatest kinetic energy at A, and the greatest gravitational potential energy at the farthest point C. It would have the same total energy (KE + PE) at all parts of its orbit, likewise the same angular momentum because it’s conserved. It would have the greatest acceleration at A, where is greatest.
Chapter 11 Ranking
1. a. A, D, B, C
b. A, D, B, C
c. A, D, B, C
Chapter 11 Exercises
2. In a water molecule, H2O, there are three atoms, two hydrogen and one oxygen.
14. Since aluminum atoms are less massive than lead atoms, more aluminum atoms than lead atoms compose a 1-kg sample.
16. (a) In both there are 27 protons (see periodic table). There are 32 neutrons in Co-59 and 33 neutrons in Co-60.
(b) The number of orbiting electrons matches the atomic number, 27.
20. Radon.
Chapter 12 Exercises
6. Density decreases as the volume of the balloon increases.
12. Aluminum has more volume because it is less dense.
22. The design to the left is better because the weight of water against the dam puts compression on the dam. Compression tends to jam the parts of the dam together, with added strength like the compression on an arch. The weight of water puts tension on the dam at the right, which tends to separate the parts of the dam.
24. A triangle is the most rigid of geometrical structures. Consider nailing four sticks together to form a rectangle, for example. It doesn’t take much effort to distort the rectangle so that it collapses to form a parallelogram. But a triangle made by nailing three sticks together cannot collapse to form a tighter shape. When strength is important, triangles are used. That’s why you see them in the construction of so many things.
Chapter 13 Ranking
2. C, B, A
Chapter 13 Exercises
14. Both blocks have the same volume and therefore displace the same amount of water.
44. The buoyant force does not change. The buoyant force on a floating object is always equal to that object’s weight, no matter what the fluid.
Chapter 14 Exercises
20. Drinking through a straw is slightly more difficult atop a mountain. This is because the reduced atmospheric pressure is less effective in pushing soda up into the straw.
28. Objects that displace air are buoyed upward by a force equal to the weight of air displaced. Objects therefore weigh less in air than in a vacuum. For objects of low densities, like bags of compressed gases, this can be important. For high-density objects like rocks and boulders the difference is usually negligible.
38. The end supporting the punctured balloon tips upwards as it is lightened by the amount of air that escapes. There is also a loss of buoyant force on the punctured balloon, but that loss of upward force is less than the loss of downward force, since the density of air in the balloon before puncturing was greater than the density of surrounding air.