Category: falling balls

In what sense is the Space Shuttle falling toward the earth?

When the space shuttle circles the earth, it’s experiencing only one force: the force of gravity. As a result, it’s perpetually accelerating toward the earth’s center. If it weren’t moving initially, it would begin to descend faster and faster until…splat. But it is moving sideways initially at an enormous speed. While it accelerates downward, that acceleration merely deflects its sideways velocity slightly downward. Instead of heading off into space, it heads a little downward. But it never hits the earth’s surface. Instead, it arcs past the horizon and keeps accelerating toward the center of the earth. In short, it orbits the earth—constantly accelerating toward the earth but never getting there.

Why is force = mass * acceleration an exact relationship (i.e. why not force = 2 * mass * acceleration)?

The answer to this puzzle lies in the definition of force. How would you measure the amount of a force? Well, you would push on something with a known mass and see how much it accelerates! Thus this relationship (Newton’s second law) actually establishes the scale for measuring forces. If your second relationship were chosen as the standard, then all the forces in the universe would simply be redefined up by a factor of two! This redefinition wouldn’t harm anything but then Newton’s second law would have a clunky numerical constant in it. Naturally, the 2 is omitted in the official law.

Does air resistance affect a horizontally thrown ball?

Yes. A ball thrown horizontally gradually loses its downfield component of velocity. For that reason, you must throw a ball somewhat below the 45° angle from horizontal in order to make it travel as far as possible. Actually, the air has even more complicated effects on spinning balls.

Is it possible for a ball to fall to earth at a different angle from the one at which it rose?

If the ground is level and there were no air resistance, the answer would be no. The flight of the ball is perfectly symmetric. It rises to a maximum height in a parabolic arc and then returns to the ground as the continuation of that same parabolic arc.

However, if the ground isn’t level, then the angle it hits the ground at might be different. For example, if you toss a ball almost horizontally off a cliff, it will hit the ground almost vertically. Horizontal and vertical are two very different directions.

Air resistance also tends to slow a ball’s motion and it’s particularly effective at stopping the downfield component of its velocity. Gravity makes sure that the ball descends quickly, but there is no force to keep the ball moving downfield against air resistance. The result is that balls tend to drop more sharply toward the ground. When you hit a baseball into the outfield, it may leave your bat at a shallow angle but it will drop pretty vertically toward the person catching it.

Finally, if the ball is spinning, it can obtain special forces from the air called lift forces. These forces can deflect its path in complicated ways and are responsible for curve balls in baseball, slices and hooks in golf, and topspin effects in tennis.

Why on Pg. 6, 2nd full paragraph, it says the car is accelerating if the slope of the road changes but in the “not accelerating” list it says a bicycle going up a hill is not accelerating. Aren’t those the same situation?

Here is why the two situations are different:

In the first case, the car is traveling on a road with a changing slope. Because the road’s slope changes, the car’s direction of travel must change. Since velocity includes direction of travel, the car’s velocity must change. In short, the car must accelerate. Picture a hill that gradually becomes steeper and steeper—the car’s velocity changes from almost horizontal to almost vertical as the slope changes.

In the second case, the bicycle is climbing a smooth, straight hill at a steady speed. Since the hill is smooth and straight, its slope is not changing. Since the bicycle experiences no change in its direction of travel or its speed, it is traveling at a constant velocity and is not accelerating.