This was received without identification. I assume it's yours, since you're the only student working at or near Asst 21. Let me know if I'm wrong.
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Asst seed 21-1
A ball is tossed vertically upward and caught at the position from which it was released.
• Ignoring air resistance will the ball at the instant it reaches its original position be traveling faster, slower, or at the same speed as it was when released?
answer/question/discussion:
I believe the ball will be traveling faster because gravity will be slowing the ball’s upward movement. When the ball starts falling, the gravity will be acting to speed up the velocity.
Gravity exerts identical forces going up and going down, which is the nature of a conservative force.
By the conditions of this problem the ball goes up exactly as far as it comes down.
So when the ball is rising, the gravitational force is opposed to motion and does negative work.
When the ball is falling, the gravitational force is in the direction of motion and does positive work.
The negative work done by gravity as the ball rises is therefore equal and opposite to the positive work done by gravity as it falls.
If gravity is the only force acting on the ball, then its KE change (being equal to the work done by the net force acting on the object) is negative when the object rises and positive when it falls, and in this case the two are furthermore equal and opposite.
So the object has the same KE when it is caught that it had when it was released.
• What, if anything, is different in your answer if air resistance is present? Give your best explanation.
answer/question/discussion:
In the presents of air resistance, the velocities both for the upward travel and downward movement will be slower than without any air friction but I still believe the velocity reaching the original position will be faster than the initial velocity upward
Air resistance is in the direction opposite motion, so whether rising or falling air resistance does negative work on the ball.
The result is that when as ball rises, its kinetic energy is all lost over a shorter distance than if air resistance was absent.
When the ball falls, gravity therefore does its positive work through a lesser distance, which alone would result in a lesser KE when the ball is caught. In addition, air resistance does negative work as the ball falls, so it gains even less KE. So the ball is caught at a velocity which is less than its release velocity.
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15 minutes of which 10 was pondering velocity and maybe KE
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See my notes on how energy conservation and the definition of work-energy apply in this situation.