Any complaints email to janovi@wm.edu.

14.) If you drop a ball onto the floor from a height of 1 m, it will rebound to a height of less than 1 m. Why can't it bounce higher than 1 m? Why doesn't it even reach 1 m?

Answer:It won't bounce higher than 1 m because energy is conserved. Raising it one meter means gravity will do (1m)mg of work on the ball when it is released. The reason it will never reach 1 m is because of friction. In an ideal world, no energy would be lost to the sound of the ball hitting the ground, thermal energy produced by the deformation of the ball, squeezing the material of the ball together, or maybe deforming the ground and sending little bits around.

28.) Why does it hurt less to land on a soft foam pad than on bare concrete after completing a high jump?

Answer: The foam pad will act as a spring plus shock absorber. Much of the kinetic energy of you falling will go into deforming the pad and not into liquefying your bones. On the other hand, concrete does NOT deform. Concrete doesn't dent easily so most of the collision energy goes into the person. Your momentum must be brought to zero by an impulse; the foam acts with a small force over a large time interval while the concrete acts with a large force over a short time, both of which bring your acceleration to zero (Just like the superhero problem from homework 1).

43.) A salad spinner is a rotating basket that dries salad after washing. How does the spinner extract the water?

Answer: The water droplets on the salad when at rest will remain fixed in place due to static friction(we're guessing there will be little friction) with the salad. Eventually, the water droplets will fly off in straight lines away from the salad when the salad is being accelerated inward and the friction of the droplets on the leaves is not sufficient to similarly accelerate them too.

56.) Most racing cars are built very low to the ground. While this design reduces air resistance, it also gives the cars better dynamic stability on turns. Why are these low cars more stable than taller cars with similar wheel spacings?

Answer: Consider a tricycle. The center of mass is kept low to the ground because friction in making a turn will produce a torque acting at the center of mass as the pivot point. Bringing the center of mass low to the ground is reducing the length of the lever arm and thus the torque.

4.) When you stand on a particular trampoline, its springy surface shifts downward 0.12 m. If you bounce on it so that its surface shifts downward 0.3 m, how hard is it pushing up on you?

Answer: We will treat the trampoline as a spring, which means there is a spring constant associated with the trampoline. When the person stands on the trampoline, gravity is pushing them down until they reach a new equillibrium which is 0.12 m down. So we know the force applied to the trampoline and the displacement. Thus, we can say that our weight alone brings the trampoline to 0.12m snd thus the force necessary to bring the tramploine 2.5 times that distance from equilibrium must be 2.5 times our weight. For those who want to see a numerical solution, we can substitute into F = -kx, and find k = -81.67m, where m is the MASS.. Next, we know the displacement when bouncing, 0.3 m, and we know k, so plugging these two numbers into the same equation, we find a force of 24.5 m/s^2 times the mass

5.) Engineers are trying to create artificial "gravity" in a ring-shaped space station by spinning it like a centrifuge. The ring is 100 m in radius. How quickly must the space station turn in order to give the astronauts inside it apparent weights equal to their real weights at the earth's surface?

Answer: This is a straight forward calculation. We start with Newton's 2nd Law. The force is just some astronaut's weight, mg. And the acceleration is centripetal. We plug these two quantities into the 2nd Law and get

7.)When you put water in a kitchen blender, it begins to travel in a 5-cm radius circle at a speed of 1 m/s. How quickly is the water accelerating?

Answer: We start with a = v^2/r and plug in the values for the speed and radius we are given. The acceleration is a = (1 m/s)^2 / (0.05 m) = 20 m/s^2

2.) You are seated in a subway car, facing forward with your eyes closed. The only way that you can tell where you are going is by feeling the effects of motioin on your body.

a.) When the car is traveling at a steady speed on a straight section of track, what is the net force on your body? Answer There is no net force on your body. This is by Newton's 2nd Law.

b.) Why is it very difficult to feel which way the car is going when it's traveling at a constant velocity? Answer: Because the human body will respond to accelerations, and when the net forces are zero, constant speed and no speed feel the same.

c.) Explain the sensations you experience as the car increases or decreases its forward speed. Answer: You will feel an additional horizontal force as you are accelerated forward or back.

d.) How can you tell when the car turns to the left or the right? Answer: You'll be pushed in the opposite direction by a fictitious force.