Suppose I throw a ball upward, it travels the maximum distance until it momentarily stops and starts falling backing down.
Now the question arises that when I throw the ball up with force F (which is definitely greater than gravitational force on the ball else it would never go up). It means force applied F minus (-) Gravitational Force Fg = let say Fu. Now when the ball reaches the maximum altitude, it starts falling down. The only force on the ball is Fg.
If we compare Fu and Fg. Fg is greater than Fu, meaning the ball falling down has more velocity than the ball going up and it would take less time to come down.
Assumptions : No air resistance. Applied force F is less than the double of Fg. Because if F is more than twice the Fg than ball going up must have more velocity than ball falling down. and if F is exactly the double of Fg, then the time for ball moving up = time taken to fall back down.
Shouldn't the ball falling down take less time than the ball going up ?
2017-07-24 6:39 pm
回答 (5)
2017-07-24 6:53 pm
✔ 最佳答案
Taking upward quantities as positive and assuming that there is no air resistance, the case is:An upward force, Fu, is applied to the ball in a very short period of time to make the initial velocity u. Then, in the whole journey, the only force acting to the ball is -Fg (i.e. acceleration a = -g), which makes the ball decelerates to stop, and then falls down to the original position.
In the going up journey, the initial velocity vₒ= u, the acceleration a = -g and the final velocity is v = 0.
In the going down journey, the initial velocity vₒ= 0, the acceleration a = -g and the final velocity v = -u.
Applying the formula: v = vₒ + at, the time for ball moving up = time taken to fall back down.
2017-07-24 9:10 pm
The force you apply when throwing the ball up, is only for the period of time when your hand is in contact with the ball. As soon as you let go, the only force on the ball is gravity (no air resistance).
You need to analyze the ball during two separate periods. #1 is while you are pushing it. #2 is while it is going up and down under only gravity.
You need to analyze the ball during two separate periods. #1 is while you are pushing it. #2 is while it is going up and down under only gravity.
2017-07-24 8:00 pm
Think conservation of energy. You don't even have to deal with force or acceleration.
kE = PE
(1/2)mv^2 = mgh
mass cancels
(1/2)v^2 = gh
So, whatever velocity you let the ball lift off in a vacuum it will return at the same velocity. There's a weird thing about this, though. I say a vacuum, but it turns out whatever friction that happens on the way up is the same on the way down, so really it doesn't have to be in a vacuum. Put another way, the only time the ball has zero velocity is right before it starts to fall, when it has used up its upward KE. It regains its KE upon falling. Velocity begin and end has the same speed just in the opposite direction.
kE = PE
(1/2)mv^2 = mgh
mass cancels
(1/2)v^2 = gh
So, whatever velocity you let the ball lift off in a vacuum it will return at the same velocity. There's a weird thing about this, though. I say a vacuum, but it turns out whatever friction that happens on the way up is the same on the way down, so really it doesn't have to be in a vacuum. Put another way, the only time the ball has zero velocity is right before it starts to fall, when it has used up its upward KE. It regains its KE upon falling. Velocity begin and end has the same speed just in the opposite direction.
2017-07-24 7:55 pm
If you consider air resistance as well you discover precisely the reverse.
On the way up we have the force of gravity and the force of friction both causing the ball to slow down.
So it slows down quickly.
On the way down the force of friction opposes the force of gravity so the ball falls more slowly.
The only exception to this is golf. In golf the spinning of the ball produces lift so it goes up for 80% of its flight and only takes 20% of its time to fall down.
On the way up we have the force of gravity and the force of friction both causing the ball to slow down.
So it slows down quickly.
On the way down the force of friction opposes the force of gravity so the ball falls more slowly.
The only exception to this is golf. In golf the spinning of the ball produces lift so it goes up for 80% of its flight and only takes 20% of its time to fall down.
2017-07-24 7:14 pm
The instant just after the ball *leaves* your hand, the only force on the ball is gravity.
During the flight the only force on the ball is gravity.
The instant just before the ball *returns* into your hand, the only force on the ball is gravity..
The height is controlled only by the speed with which the ball leaves your hand. How the ball reached this speed is irrelevant - e.g. the ball could be released from a rapidly rising balloon.
For information, there is an accelerating forice from your hand just before the ball leaves your hand. And there is a decelerating force from your hand just after the ball returns to you hand.
These 2 forces don't have to be equal. But their impulses (force x time force is applied) must be equal.
During the flight the only force on the ball is gravity.
The instant just before the ball *returns* into your hand, the only force on the ball is gravity..
The height is controlled only by the speed with which the ball leaves your hand. How the ball reached this speed is irrelevant - e.g. the ball could be released from a rapidly rising balloon.
For information, there is an accelerating forice from your hand just before the ball leaves your hand. And there is a decelerating force from your hand just after the ball returns to you hand.
These 2 forces don't have to be equal. But their impulses (force x time force is applied) must be equal.
收錄日期: 2021-04-18 17:25:54
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20170724103916AA1FTWQ