Chapter 1 Homework Answers

A. Give an example of two objects in which the lighter one falls faster than the heavier one.
E.g., crumpled small paper vs uncrumpled large paper, arrow vs basketball, a penny and a parachute, etc.

B. Give an argument against Galileo's claim that a body rolling down an inclined plane is not different in kind from one falling freely. Translated to positive form: Argue that a body rolling down an incline IS different in kind from a freely falling object, i.e., that the velocity versus time behavior IS different.
A couple of possibilities:

• Rolling with translation is different in kind from pure translation without rolling. A rolling object will roll more slowly than an object of the same size sliding, even without friction.
• A rolling object suffers three different kinds of resistance: air resistance, rolling resistance, and traction, without which the object would not roll. This last interaction, traction, is odd in that it does reduce the object's speed, but is not a "lossy" mechanism. We will see later that energy is not lost due to this tractive force. A purely falling object suffers only air resistance. Finally, a sliding object suffers two "lossy" resistances - air resistance and sliding friction.

C. What is the most significant difference between Galileo's "new physics" compared to Aristotle's "old physics"? Defend your answer. The final appeal to experiment, but experiment guided by theoretical understanding. Also, the explicit consideration of friction.

2. A sprinter does the 100-meter dash in 10.0 seconds.
a. What is his average speed? v = dx/dt = 100m / 10s = 10 m/s (~23mph)
b. If he could maintain this pace for a mile (1610 meters), what would his time for the mile be? dt = dx/v = 1610m / 10m/s = 161 s = 2min 41s, substantially faster than the 4min mile

10. A car moving at 30m/s (~67mph) brakes to a stop with acceleration -6m/s².
a. How long does it take to stop? dt = dv/a = -30m/s / -6m/s² = +5s
b. How far does it travel? v_ave = 15m/s and dx = v*dt = 15m/s *5s = 75m

11. A car travels 100 meters in 5 seconds from a standing start. Find:
a. its average speed: v = dx/dt = 100m/5s = 20m/s
b. its final speed: v_i=0 and v_ave=20m/s, so v_f=40m/s
c. its acceleration: a = dv/dt = 40m/s / 5s = +8m/s²