Exercises:
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Chapter 4:
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28: When you are standing still, the forces on you balance. This means that the downward force of gravity is exactly offset by the upward force of the ground. (Note that these are NOT an action/reaction pair. NOT! NOT! NOT!)
In order to jump up (ie: to accelerate vertically), the net force on you must be upwards. This means that the upward force on you from the ground must be larger than your weight. Note that you can increase the upward force of the ground on you by increasing the force that you exert on the ground (since these two forces ARE an action/reaction pair).
30: The acceleration of a rock at the top of its trajectory is 10 m/s^2
downward, just like it is at all other times in its flight (neglecting air
resistance).
Acceleration is the CHANGE in velocity. If the acceleration is zero, then
the velocity is not changing.
36: No, a stick of dynamite does not CONTAIN force. When the dynamite explodes, it can exert a force on other objects. Force is not an inherent property of any object. It is incorrect to say that anything 'contains a force'.
Chapter 5:
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2: Action reaction pairs (the order of each pair is irrelevant):
a) the force of the hammer on the nail and the force of the nail on the hammer.
b) The gravitational force pulling the book toward the Earth and the gravitational
force pulling the Earth toward the book.
c) The downward force on the air from the helicopter blade and the upward
force on the helicopter blade from the air.
8: The scale reads 100 N. There are two types of accepted reasons for this: a) we saw it demonstrated in class, and b) one weight serves to keep the scale motionless while it supports the second weight, therefore the scale only reads the weight of the second weight. (In general, I will accept the explanation 'we saw it demonstrated in class' as an acceptable explanation for most homework problems and tests [assuming of course that a: we did demonstrate it and b: it happened like you remember].)
10: The downward pull of gravity and the upward support force from the floor are equal and opposite. We know this because the person standing still has no acceleration, therefore the total force acting on her is zero.
These are NOT an action reaction pair. There are two action reaction pairs here: a) The gravitational force pulling her to the Earth and the gravitational force pulling the Earth toward her and b) the upward force from the floor on her and the downward force from her on the floor. Note that when considering her motion, we only consider the forces acting on her. We don't care about the forces that she exerts on the floor and on the Earth.
24: This is a third law example. Person A exerts a force on person B (via the rope) therefore person B exerts an equal and opposite force on person A. Since there is no friction, there are no other horizontal forces acting. This means that persons A and B have the same total force acting on each of them. Since they also have the same mass, they will have the same acceleration. Therefore they will meet exactly in the middle.
Note that if person A is much heavier, although the total force will still be the same, his acceleration will be much less and person B will be pulled farther than person A.
Note also that very few tug-of-wars are played on slippery ice. In a real tug-of-war, what matters most is how much traction you have (how hard you can push against the ground and resist being pulled into the center).
32: If you are standing in a bus that moves at constant velocity and drop a ball, you will see it fall vertically. Your friend will see it fall diagonally, just like you threw it with the same horizontal speed that the bus has.
Problems:
Chapter 4:
6: If it takes four times as much force to make the second box have the same acceleration as the first, then the second box must have four times as much mass as the first. Remember that F = ma. If a is the same but F is four times larger, then m must also be four times larger.
8: You need to think about the total force on the skydiver. Gravity is pulling downward with a force equal to her weight. Air resistance is pushing upward with a force equal to half her weight. Thus the net force on her is the sum of the two forces: F(net) = weight (down) + 1/2 weight (up) = 1/2 weight (down). Thus, the net force on her is only half the force of gravity. Thus, her acceleration will only be half as great as gravity or 5 m/s^2.
Chapter 5:
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2: If you push on the wall with 30 N, then the wall pushes on you with 30 N. (The wall does not go anywhere because it is a anchored to the Earth and a 30 N force on the Earth will not make it move very much.) The total horizontal force on you is 30 N (since there is no friction) so you will accelerate.
F = ma so that a = F/m = 30 N / 60 kg = 30 kg m/s^2 / 60 kg = 0.5 m/s^2
Note a) 1 N = 1 kg m/s^2 and b) you will not be able to push on the wall for very long since you will rapidly move away from it.