phy 121
Your 'cq_1_23.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
A wad of paper is dropped from a second-story balcony and falls through still air to the ground.
As it speeds up, what happens to the air resistance it encounters?
answer/question/discussion:
See my question I added to this from seed 21.1. I think I need that cleared up before I can answer this one. If I understand correctly then air resistence increases as an object falls. It has an opposing effect on PE. PE can’t decrease as much and KE can’t increase as much resulting in velocity not increasing as much as it would if there was no air resistence. The answer to the question though is as the object speeds up air resistance increases.
The force of air resistance increases as the speed of the object with respect to the air increases. Thus the force of air resistance increases as the object falls.
The PE change is due only to the force of gravity, and is not affected by a resistance.
The KE change is due to the net force, and air resistance is part of this force.
There is a PE loss, which tends to increase the KE of the falling object. Air resistance does negative work on the falling object, and therefore tends to decrease the KE. In this case the PE loss exceeds the work done by air resistance, so KE does in fact increase, but by an amount less than the PE loss.
and the force of air resistance is nonconservative.
The net force in the direction of motion is less than the gravitational force, which is also in the direction of motion. So the work done by the net force on the object is less than the work done by the gravitational force. *&$*&$
What happens to the net force acting on it?
answer/question/discussion:
The net force pulling it back to the ground decreases. The PE of gravity decreases. Which makes sense if what I said above is correct. Fnet = m* a. I am essentially saying that a is decreased (velocity doesn’t increase as fast) and if a is decresed then Fnet will also decrease
F_net is the resultant of the gravitational force and the force of air resistance.
The gravitational force acts in the direction of motion, downward, while the air resistance acts in the direction opposed to motion, in this case upward.
The increasing air resistance therefore decreases the magnitude of the net force. The net force remains downward, but decreases in magnitude as the velocity increases.
What happens to its acceleration?
answer/question/discussion:
Oh, I just answered that. I think I am on a roll!
The acceleration is originally equal to the acceleration of gravity, but after the initial instant the increasing speed results in an increasing force of air resistance. The resulting decrease in the magnitude of the net force implies (by Newton's Second Law) a decrease in the magnitude of the acceleration.
If it dropped from a much higher point, what would happen to the net force and the acceleration?
answer/question/discussion:
Both would decrease more (I think), because the air resistance will keep on increasing, making acceleration slower and slower, therefore decreasing the net Force.
Theoretically is it possible for air resistance to stop an object? If it keeps increasing, could it eventually counteract the Fnet and stop acceleration all together? It’s not anything that makes sense to me, in that it isn’t anything I have ever experienced, but is it possible in some circumstance that I am not aware of? Or, am I just so wrong about all of this that it isn’t even funny?
Acceleration can approach zero, but that doesn't stop the object. Just keeps it from speeding up any more.
The object will keep speeding up, but at a lesser and lesser rate (as you say).
If the object speeds up enough (as it will if the fall is far enough) the air resistance will eventually approach the weight of the object, so the net force will approach zero and acceleration will approach zero.
The acceleration is originally that of gravity; as the speed of the falling object increases the acceleration approaches zero.
** **
15 mins
** **
This is part of my response to seed question 21.1 And your comments. I inserted a follow-up question.
I think the air resistance will be the same going up and coming down, so it will still act in the same way, the difference will be that the air resistance will increase the effects of gravity going up causing it to slow down quicker, but the air resistance will decrease the effects of gravity coming down so it will speed up slower. The end result would be that it travels less distance, but will still return at the same speed it was going when it was released.
Air resistance will enhance the slowing effect of gravity on the rising ball, which will as a result not rise as far. As a result of the decreased maximum height, the falling ball won't drop as far, resulting in a lesser final speed.
&&& The ball will still drop the same distance as it goes up. It won't go up as far as it would have if there had been no air resistence, but it will then fall the same distance it went up, so unless air resistence is stronger coming down why would it have an increased effect and result in a lower velocity on return? Does air resistence have more of an effect as the velocity increases, as the object is coming back down?
The situation is not symmetric.
On the way up the air resistance slows the ball more rapidly, resulting in a change of speed which is greater than it would be in the absence of air.
On the way down the air resistance prevents the ball from speeding up as rapidly, resulting in a change of speed which is less than it would be in the absence of air.
On the way up the force of air resistance is in the same direction as the gravitational force, so the net force is of greater magnitude than the gravitational force.
On the way down the force of air resistance is in the direction opposite the gravitational force, so the net force is of lesser magnitude of the gravitational force.
The negative work done on the ball on the way up is of greater magnitude than the positive work done on the ball on the way down.
Air resistance will then oppose the speeding up of the falling ball, so that the final velocity will be even less.
For a dense ball tossed gently upward, the effect of air resistance will be small, perhaps negligible with respect to the accuracy of our instruments. If the ball is less dense, and/or speeds are greater, air resistance will have a greater effect.
In terms of energy conservation, assuming still air (i.e., no wind, no rising and falling of air), air resistance acts always in the direction opposite motion and therefore does negative work on the object. PE doesnt change between the beginning and the end of the interval, so the result is a lesser KE at the end than at the beginning.
************* This note is added to each submission to ensure that the instructor has reviewed your work. The instructor must manually remove this note. If it hasn't been removed, and if the instructor has not made specific responses, then it is possible that your work hasn't been properly reviewed and you should notify the instructor to be sure.
Your responses have been reviewed and everything looks good.
Please let me know if you have any questions related to this orientation assignment.
*&$*&$