Physics 105N - How Things Work - Fall, 1997

Problem Set 3

• Due Monday, November 10, 1997, in class
• Please answer each problem as concisely as possible
• You may discuss the problems with one another but you must write them up separately and in your own words.
• In addition to points below, you will receive 5 points if you print your name neatly and legibly.

1. As the spaceship turns left, the crew will be thrown to the right (actually, as the spaceship turns left, the crew will tend to keep going straight ahead--but this is "to the right" in the spaceship frame of reference).
2. The guard should fall backward (opposite to direction of motion of the projectile). If the projectile carries enough momentum to push the alien back, it will throw the guard back too.
3. The wings of the spacecraft do no good in space, because there's no air. If the exhaust is thrown out the rear, the spacecraft can only move forward. To turn, it would need to throw exhaust out the side.
4. You're right because the spaceship would have to propel most of its mass (in the form of exhaust) out the back (and at high speed) just to leave the Earth. The stages are the empty fuel containers. It wouldn't be able to take off again from a big planet without refueling. (To leave the moon is possible, because its gravity is much less than Earth.)
5. If she lands on the wing, the plane must be going horizontally. Therefore, the force upward from the wing to stop her is just as great as the force upward from the ground would be, and she would still die. [If she was rescued far above the ground, she might survive, because she might not be going very fast. Or, if there were enough room, the plane could move partly vertically downward, catch the girl, then slow down gradually, reducing the average force.]

1. Both you and the book are in free fall, so from your point of view, the book seems to be just hovering in front of you. This is the same as in deep space--the gravity and the free fall cancel each other out, and it's just like no gravity at all.
2. It's easy. You just have to push down slightly on the elevator, and it will go a little faster down. It will push back on you, and you'll go a little slower down, which will make you move up relative to the elevator.
3. The elevator is now accelerating upward, so unless you are holding on very, very tight to the ceiling, the floor will come right up to meet you. In other words, you'll be thrown to the floor.
4. Yes, it is possible to lift yourself with the multiple pulley. The multiple pulley reduces the force required to lift the object, so if you're strong enough, and pull a long length of rope through your hands as you ascend, you'll go up the desired distance.

"A mountain climber uses a rope…"

Every time you start or stop, you are accelerating. To do this, there must be a net force on you, so the rope force (tension) must either be greater than or less than your weight. The first case, which we are concerned with, is when you are accelerating upwards. For example, when you are at rest and then start climbing up, then you are accelerating upwards. Another case is when you are going down, and then slow to a stop. In both of these cases, the rope is exerting a force greater than your weight.

1. Explain why a bicycle is unstable when it's stationary [5 points]

It's theoretically possible to balance the bike, by putting the center of mass over the line defined by the tires. But it's unstable, because any small deviation from this will cause it to go even further away from balance. This is like trying to balance a pencil on its point.

2. Explain two effects that a moving bicycle exhibits which make it almost steer itself [5 points]

1. When you tilt the bike over, the front wheel turns in the direction of the tilt. (This is because of the way the front fork is constructed.) The front wheel doesn't need to be spinning for this.
2. When the front wheel is rotating, and the bike starts to tilt to the right, the front wheel precesses (turns of its own accord). This, again, is to the right.