Imagine you are riding on a train that is moving along at a constant speed in the forward direction. You are facing forward and holding a ball out beside you.
1. If you drop the ball, which way does it fall from your perspective?
Answer: It falls straight down and lands directly at your side.
Why: Since the train is not accelerating you are in an inertial frame of reference. From your perspective the balls initial velocity is zero (its velocity relative to you). When you drop it the only force acting is the downward pull of gravity, so the ball falls straight down.
2. From the perspective of someone standing still next to the track, with the train moving from left to right in front of them, which way does the ball fall?
Answer: From this perspective the ball will move to the right as it falls.
Why: The ball has a constant velocity to the right relative to the person beside the train. When you drop the ball the person beside the track will see it being accelerated toward the ground by gravity, but it will continue to move to the right with its original speed as it falls.
3. If the train's engineer applies the breaks while the ball is falling, where will the ball hit the train car's floor? Why? Assume that the static friction between you feet and the train car's floor is strong enough to keep you from sliding.
Answer: It will hit in front of you since the train and you experience a horizontal acceleration toward the back of the train (a deceleration), while the ball experiences no acceleration in the horizontal direction since it is in the air.
Why: From the balls perspective the train is accelerating in reverse giving it a velocity relative to the ball in the reverse direction.
4. Having grown tired of bouncing the ball you decide to take a nap. You sit down next to a window and fall asleep. When you wake up you look out the window to see another train passing. It appears to be moving at constant velocity toward the front of your train. You don't feel yourself accelerating so your train must also be moving at constant velocity. Without looking out any other windows, so that all you see is the passing train, can you tell the velocity of your train relative to the ground?
Answer: No. You only know the relative velocity of the two trains.
Why: Without looking at the ground you cannot tell how fast you are moving relative to it, you are in an inertial frame of reference. In fact, you cannot even tell which direction you are traveling relative to the ground. You could be moving forward and the train next to you could be moving forward at a higher speed. You may be stopped with the train next to you moving forward. Or, you could even be moving backward with the train next to you stopped.
In a common circus stunt a man is shot out of a canon. In this stunt the canon is placed at an angle so that the man flies through the air in front of the audience in a long arc. Neglect air resistance for this problem.
5. What is the direction of the fictitious force on the stunt man as he flies through the air?
Answer: The fictitious force points straight up.
Why: As the stunt man flies through the air he is accelerated downward by the force of gravity. The fictitious force points in the direction opposite this acceleration.
6. What is his apparent weight?
Answer: Zero.
Why: The fictitious force exactly balances the force due to gravity and he feels weightless.
7. He lands on a thick foam pad. Why does this protect him from injury?
Answer: The foam pad has two beneficial effects, it spreads the force needed to stop him out over a large area of his body and it applies the force over a long distance.
Why: The foam pad deforms to the shape of the stunt man's body, which allows the force to be applied over a large area. If he were to hit a flat rigid surface the force would be much more localized (remember the dropped egg). Also the foam pad compresses just like a spring allowing the force to be applied over a longer distance than in the case when he hits a rigid object. In order to remove the stunt man's kinetic energy, to stop him, work must be done on him. If this work is done over a large distance only a small force is required. In contrast, a rigid object barely moves at all and so it applies an enormous force, ouch!
8. If he doesn't bounce off of the pad where has the kinetic energy he had just before landing gone?
Answer: Most of his kinetic energy has been transformed into thermal energy.
Why: Since he doesn't bounce he has no rebound energy so all of his kinetic energy has been converted into other forms. Most of it is converted into thermal energy in the foam pad; the pad heats up a bit. Some of it may also be radiated as sound; you may hear a thump as the stunt man hits the pad.