Category: falling balls

When you throw a ball upward, what force pushes it upward?

To throw the ball upward, you temporarily push upward on it with a force greater than its weight. The result is that the ball has a net force (the sum of all forces on the ball) that is upward. The ball responds to this upward net force by accelerating upward. You continue to push upward on the ball for a while and then it leaves your hand. By that time, it’s traveling upward with a considerable velocity. But once it leaves your hand, it is in free fall. Nothing but gravity is pushing on it—it’s carried upward by its own inertia! In fact, it’s accelerating downward at 9.8 m/s^2. It rises for a while, but less and less quickly. Eventually it comes to a stop and then it begins to descend.

If the Space Shuttle is always falls toward the center of the earth, how does it get to outer space? If something accelerates, doesn’t it go faster and thus have its speed increase?

The second question first: no, an object can accelerate without going faster. In fact, a stopping object is accelerating! If an accelerating object can speed up or slow down, it can certainly maintain a constant speed. If you swing a ball around in a circle on a string, that ball is accelerating all the time but its speed isn’t changing.

Now the first question: for the space shuttle to reach orbit, it needs an additional force in the upward direction. It obtains that force by pushing exhaust gas downward so that the exhaust gas pushes it upward. During the time when it’s heading toward orbit, it’s not falling because it has an extra upward force on it. However, the Space Shuttle can leave its orbit and head off into outer space by traveling faster than it normally does. It acquires this increased speed by firing its rocket engines again. Its usual speed keeps it traveling in a circle near the earth’s surface. If it went a bit faster, its path wouldn’t be bent downward as much and it would travel more in a straight line and away from the earth. It would still be falling toward the earth (meaning that it would still be accelerating toward the earth), but its inertia would carry it farther away from the earth. If the Shuttle had enough speed, it would travel to the depths of space before the earth had time to slow its escape and bring it back.

While gravity supposedly makes all objects accelerate at the same rate, feathers do not seem to comply. What factors affect the feather’s acceleration, besides air resistance (which should affect all objects equally)?

Actually, air resistance doesn’t affect all objects equally. The feather has so much surface area that it pushes strongly on the air through which it moves and the air pushes back. For an object with very little mass and weight, the feather experiences an enormous amount of air resistance and has great difficulty moving through the air. That’s why it falls so slowly. If you were to pack a feather into a tiny pellet, it would then fall just about as fast as other objects. Similarly, you fall much more slowly when your parachute is opened because it then interacts with the air much more effectively.

If you drop a penny from the Empire state building – could it really puncture a hole in a car because of its constant acceleration?

Probably not. If the penny were to fall sideways, so that it had as little air resistance as possible, it would reach about 280 km/h (175 mph). That speed ought to be enough to drive the penny into the car if its top were thin enough. However, studies have shown (see http://www.urbanlegends.com/science/penny_falling_impact.html) that coins tumble as they fall and experience substantial air resistance. As a result, you could probably catch a falling penny in your hand, although it might sting a bit. A falling ballpoint pen, because of its aerodynamic shape, is another matter.

Why do objects on earth accelerate downward at the same speed regardless of their mass?

What you mean here is that they accelerate downward at the same rate (“speed” has a particular meaning that isn’t so well suited to discussions of acceleration). This fact comes about because, although massive objects are harder to accelerate, they also experience more weight. Thus a huge stone will fall at the same rate as a small rock because the stone will be pulled downward more strongly by gravity and that extra pull will make up for the stone’s greater inertia.

If you dropped a bullet and at the same time, fired a bullet directly at the ground, wouldn’t the bullet fired at the ground hit the ground first?

Sure it would. The fired bullet will only hit the ground at the same time as the dropped bullet if the fired bullet is shot exactly horizontally. If you fire the bullet at the ground, then it starts out with an enormous downward component to its velocity. The falling bullet doesn’t have this initial downward component to its velocity and never catches up.

Why do two objects of unequal mass fall and hit the ground at the same time?

If one object has twice the mass of the other, then it is twice as hard to accelerate. To make it keep pace with the other ball, it must experience twice the force. Fortunately, gravity pulls on it twice as hard (it has twice the weight of the other ball), so in falling, it does keep pace with the other ball. The two fall together. Just for fun, imagine stepping off the high diving board with two friends. The three of you have essentially identical masses and weights and also fall at the same rate. Now imagine that two of you hold hands as you fall. You are now a single object with twice the mass of your other friend. Nonetheless, you still fall at the same rate. So an object with twice the mass of another falls at the same rate as that other object.

If you fire a bullet horizontally and drop an identical bull at the same moment, will they both hit the ground at the same time?

Yes. The fired bullet may travel farther, but it will fall just as quickly as the dropped bullet and they’ll hit the ground at the same moment. This effect explains why you must aim above the target when shooting at something far away. The faster the bullet travels to the target, the less it will drop. An arrow travels slowly enough that it will fall a considerable distance en route. You must aim quite high when shooting an arrow.

Why do you feel no acceleration in free fall, even though you are accelerating?

This wonderful question has many answers. The first, and most direct, is that you do feel the acceleration. You feel an upward fictitious force (not a real force at all, but an effect of inertia) that exactly balances your downward weight. The feeling you experiences is “weightlessness.” That’s why your stomach feels so funny. You’re used to having it pulled downward by gravity but the effect of your fall is to make it feel weightless.

If you had an object in an empty sphere with a radius of a few miles, surrounded by equally distributed and very concentrated mass, what effects of gravity would the object feel?

As long as the mass isn’t so concentrated that the laws of general relativity become important, the object won’t feel any gravity at all. The forces from opposite sides of the surrounding mass will cancel exactly. For example, if you were at the center of the earth in a large spherical opening, you would be perfectly weightless. The force from the north side of the earth would balance the force from the south side. This effect is quite remarkable and depends on the fact that gravity becomes weaker as the inverse square of the distance separating two objects. That way, even if you aren’t in the exact center of the earth, the forces still cancel.