#$&*
Phy 121
Your 'cq_1_18.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
________________________________________
A child in a slowly moving car tosses a ball upward. It rises to a point below the roof of the car and falls back down, at which point the child catches it. During this time the car neither speeds up nor slows down, and does not change direction.
• What force(s) act on the ball between the instant of its release and the instant at which it is caught? You can ignore air resistance.
answer/question/discussion: ->->->->->->->->->->->-> :
The instant the ball is released the work done against gravity by the child moves the ball upward, the force of gravity against the ball begins working against the work done by the child. Once the ball reaches the point where it begins to fall back down, the force exerted by gravity pushes the ball down until the child catches it and the child’s hand exerts an equal force on the ball to catch it in their hand.
#$&*
• What happens to the speed of the ball between release and catch? Describe in some detail; a graph of speed vs. clock time would also be appropriate.
answer/question/discussion: ->->->->->->->->->->->-> :
The ball begins by accelerating from rest to its maximum velocity before the force of gravity working against it begins decelerating the ball to 0 m/s, at which point gravity forces the ball downward accelerating it in the negative direction until it reaches the child’s hand, at which point the ball again comes to rest.
#$&*
• Describe the path of the ball as it would be observed by someone standing along the side of the road.
answer/question/discussion: ->->->->->->->->->->->-> :
The ball would go up straight into the air, the car would move slightly further from the ball and the ball would move slightly horizontally as the ball rose and fell back down into the child’s hand
#$&*
• How would the path differ if the child was coasting along on a bicycle? What if the kid didn't bother to catch the ball? (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point)
answer/question/discussion: ->->->->->->->->->->->-> :
It would differ it the bike was moving at a faster speed because the ball would not be traveling that fast vertically and would go up but would land behind the child on the ground.
#$&*
• What if the child drops the ball from the (inside) roof of the car to the floor? For the interval between roof and floor, how will the speed of the ball change? What will be the acceleration of the ball? (You know nothing about what happens after the ball makes contact with the floor, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
The speed of the ball will change at the rate of 980 cm/s until it reaches the floor.
#$&*
• What if the child holds the ball out of an open window and drops it. If the ball is dense (e.g., a steel ball) and the car isn't moving very fast, air resistance will have little effect. Describe the motion of the ball as seen by the child. Describe the motion of the ball as seen by an observer by the side of the road. (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
The child would see the ball drop from his hand and hit the ground, the car may move a slight distance away from the ball. The observer would see the same.
#$&*
** **
10 min.
** **
October 20, 2011 at 12:54 p.m.
________________________________________
A child in a car tosses a ball upward so that after release it requires 1/2 second to rise and fall back into the child's hand at the same height from which it was released. The car is traveling at a constant speed of 10 meters / second in the horizontal direction.
• Between release and catch, how far did the ball travel in the horizontal direction?
answer/question/discussion: ->->->->->->->->->->->-> :
.5 s * 10 m/s = 5 m
#$&*
• As observed by a passenger in the car, what was the path of the ball from its release until the instant it was caught?
answer/question/discussion: ->->->->->->->->->->->-> :
Up and Down
#$&*
• Sketch the path of the ball as observed by a line of people standing along the side of the road. Describe your sketch. What was shape of the path of the ball?
answer/question/discussion: ->->->->->->->->->->->-> :
It would look like >, except wider, with the point facing upward.
@& Right idea, but it would gradually slow in the vertical direction before stopping for an instant, then gradually speeding up as it fell. This makes the path a smooth arc; there would be no point.*@
#$&*
• How fast was the ball moving in the vertical direction at the instant of release? At that instant, what is its velocity as observed by a line of people standing along the side of the road?
answer/question/discussion: ->->->->->->->->->->->-> :
`dt = .25 s, v0 = 0 m/s, a = 9.8 m/s^2, vf = 2.45 m/s
Descent
9.8 m/s^2 * .25 = 2.45 m/s
vAve = 2.45 m/s / 2 = 1.2 m/s
`ds = 1.2 m/s * .25 s = .3 m
vf = 0 m/s, `ds = .3 m, `dt = .25 s
vAve = .3 m / .25 s = 1.32 m/s
`dv = 1.32 m/s * 2 = 2.64 m/s
a = 2.64 m/s / .25 s = 10.56 m/s^2
v0 = sqrt(0 m/s ^2 + 2 * 10.56 m/s^2 * .3 m) = 2.5 m/s
It would appear to rise slower than it is progressing horizontally.
#$&*
• How high did the ball rise above its point of release before it began to fall back down?
answer/question/discussion: ->->->->->->->->->->->-> :
v0 = 2.5 m/s, vf = 0 m/s, `dt = .25 s, vAve = 1.25 m/s
`ds = 1.25 m/s * .25 s = .3 m
#$&*
*#&!*#&!
@& Good thinking and good work, but see my notes and be sure to read the information in the links below.
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
#$&*
Phy 121
Your 'cq_1_18.1' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** **
________________________________________
A child in a slowly moving car tosses a ball upward. It rises to a point below the roof of the car and falls back down, at which point the child catches it. During this time the car neither speeds up nor slows down, and does not change direction.
• What force(s) act on the ball between the instant of its release and the instant at which it is caught? You can ignore air resistance.
answer/question/discussion: ->->->->->->->->->->->-> :
The instant the ball is released the work done against gravity by the child moves the ball upward, the force of gravity against the ball begins working against the work done by the child. Once the ball reaches the point where it begins to fall back down, the force exerted by gravity pushes the ball down until the child catches it and the child’s hand exerts an equal force on the ball to catch it in their hand.
#$&*
• What happens to the speed of the ball between release and catch? Describe in some detail; a graph of speed vs. clock time would also be appropriate.
answer/question/discussion: ->->->->->->->->->->->-> :
The ball begins by accelerating from rest to its maximum velocity before the force of gravity working against it begins decelerating the ball to 0 m/s, at which point gravity forces the ball downward accelerating it in the negative direction until it reaches the child’s hand, at which point the ball again comes to rest.
#$&*
• Describe the path of the ball as it would be observed by someone standing along the side of the road.
answer/question/discussion: ->->->->->->->->->->->-> :
The ball would go up straight into the air, the car would move slightly further from the ball and the ball would move slightly horizontally as the ball rose and fell back down into the child’s hand
#$&*
• How would the path differ if the child was coasting along on a bicycle? What if the kid didn't bother to catch the ball? (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point)
answer/question/discussion: ->->->->->->->->->->->-> :
It would differ it the bike was moving at a faster speed because the ball would not be traveling that fast vertically and would go up but would land behind the child on the ground.
#$&*
• What if the child drops the ball from the (inside) roof of the car to the floor? For the interval between roof and floor, how will the speed of the ball change? What will be the acceleration of the ball? (You know nothing about what happens after the ball makes contact with the floor, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
The speed of the ball will change at the rate of 980 cm/s until it reaches the floor.
#$&*
• What if the child holds the ball out of an open window and drops it. If the ball is dense (e.g., a steel ball) and the car isn't moving very fast, air resistance will have little effect. Describe the motion of the ball as seen by the child. Describe the motion of the ball as seen by an observer by the side of the road. (You know nothing about what happens after the ball makes contact with the ground, so there's no point in addressing anything that might happen after that point).
answer/question/discussion: ->->->->->->->->->->->-> :
The child would see the ball drop from his hand and hit the ground, the car may move a slight distance away from the ball. The observer would see the same.
#$&*
** **
10 min.
** **
October 20, 2011 at 12:54 p.m.
________________________________________
A child in a car tosses a ball upward so that after release it requires 1/2 second to rise and fall back into the child's hand at the same height from which it was released. The car is traveling at a constant speed of 10 meters / second in the horizontal direction.
• Between release and catch, how far did the ball travel in the horizontal direction?
answer/question/discussion: ->->->->->->->->->->->-> :
.5 s * 10 m/s = 5 m
#$&*
• As observed by a passenger in the car, what was the path of the ball from its release until the instant it was caught?
answer/question/discussion: ->->->->->->->->->->->-> :
Up and Down
#$&*
• Sketch the path of the ball as observed by a line of people standing along the side of the road. Describe your sketch. What was shape of the path of the ball?
answer/question/discussion: ->->->->->->->->->->->-> :
It would look like >, except wider, with the point facing upward.
@& Right idea, but it would gradually slow in the vertical direction before stopping for an instant, then gradually speeding up as it fell. This makes the path a smooth arc; there would be no point.*@
#$&*
• How fast was the ball moving in the vertical direction at the instant of release? At that instant, what is its velocity as observed by a line of people standing along the side of the road?
answer/question/discussion: ->->->->->->->->->->->-> :
`dt = .25 s, v0 = 0 m/s, a = 9.8 m/s^2, vf = 2.45 m/s
Descent
9.8 m/s^2 * .25 = 2.45 m/s
vAve = 2.45 m/s / 2 = 1.2 m/s
`ds = 1.2 m/s * .25 s = .3 m
vf = 0 m/s, `ds = .3 m, `dt = .25 s
vAve = .3 m / .25 s = 1.32 m/s
`dv = 1.32 m/s * 2 = 2.64 m/s
a = 2.64 m/s / .25 s = 10.56 m/s^2
v0 = sqrt(0 m/s ^2 + 2 * 10.56 m/s^2 * .3 m) = 2.5 m/s
It would appear to rise slower than it is progressing horizontally.
#$&*
• How high did the ball rise above its point of release before it began to fall back down?
answer/question/discussion: ->->->->->->->->->->->-> :
v0 = 2.5 m/s, vf = 0 m/s, `dt = .25 s, vAve = 1.25 m/s
`ds = 1.25 m/s * .25 s = .3 m
#$&*
*#&!*#&!
@& Good thinking and good work, but see my notes and be sure to read the information in the links below.
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#
&#See any notes I might have inserted into your document, and before looking at the link below see if you can modify your solutions. If there are no notes, this does not mean that your solution is completely correct.
Then please compare your old and new solutions with the expanded discussion at the link
Solution
Self-critique your solutions, if this is necessary, according to the usual criteria. Insert any revisions, questions, etc. into a copy of this posted document. Mark any insertions with &&&& so they can be easily identified.If your solution is completely consistent with the given solution, you need do nothing further with this problem. &#