Category: falling balls

The physics and science of falling balls

If you shot a gun and dropped a bullet at the same time, how could they land at …

Lou Bloomfield Leave a comment

If you shot a gun and dropped a bullet at the same time, how could they land at the same time? Wouldn’t the acceleration behind the bullet keep it in the air longer?

If you shot the bullet horizontally, it really would hit the ground at the same time as the bullet you simply dropped. During the firing, the bullet would accelerate like crazy, but only horizontally. It would leave the gun with a velocity that was only in the horizontal direction. With no forces pushing on it horizontally after that (we’ll neglect air resistance), the bullet will make steady progress downfield. But at the same time, it will begin to fall. The vertical component of its velocity will gradually increase in the downward direction as it falls. Like the dropped bullet, it will drift downward faster and faster and the two will hit the ground together.

Why is 45° above horizontal the ideal angle to throw something the greatest …

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Why is 45° above horizontal the ideal angle to throw something the greatest distance if gravity is acting on the vertical direction but not the horizontal?

The 45° angle is ideal because it gives the ball a reasonable upward component of velocity and also a reasonable downfield component of velocity. The upward component is important because it determines how long the ball will stay off the ground. The downfield component is important because it determines how quickly the ball will travel downfield. If you use too much of the ball’s velocity to send it upward, it will stay off the ground a long time but will travel downfield too slowly to take advantage of that time. If you use too much of the ball’s velocity to send it downfield, it will cover the horizontal distances quickly but will stay of the ground for too short a time to travel very far. Thus an equal balance between the two (achieved at 45°) leads to the best distance. Note that this discussion is only true in the absence of air resistance.

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

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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…

Lou Bloomfield Leave a comment

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.