Phy 231
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.
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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: ->->->->->->->->->->->-> :
gravitational force
weight
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• 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: ->->->->->->->->->->->-> :
As the ball falls, it speeds up. As the ball rises, it slows down.
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• 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 speeds up vertically but not horizontally. The ball is moving forward at a constant speed. When it rises, it tends to fall.
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• 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 depends on the speed. With a lower speed, air resistance will not change too much at all. If it has a larger speed, the ball will accelerate backwards.
From the child's point of view the ball accelerates backwards; from the point of view of the air the ball keeps moving forward but it slows, so while the velocity remains 'forward' its acceleration is in the 'backward' direction.
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• 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 horizontal speed will be the same and the initial vertical speed will be 0 and it will increase at 9.8 m/s/s as it falls.
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• 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: ->->->->->->->->->->->-> :
There wont be much of an affect if there is no air resistance. The motion of the ball as seen by the child will be just dropped straight down. The motion of the ball as seen by an observer by the side of the road is that the ball will curve down until it hits the road.
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30 mins
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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: ->->->->->->->->->->->-> :
The ball will travel at 10 m/s horizontally and it will travel 5 meters.
ds = vAve *dt
ds = 10 m/s * 0.5 sec
ds = 5 m
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• 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: ->->->->->->->->->->->-> :
There will be a curved path. The velocity will go up slowly and then fall quickly.
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• 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: ->->->->->->->->->->->-> :
The shape is a curved path.
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• 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: ->->->->->->->->->->->-> :
a = 9.8 m/s/s
dt = 0.5 sec
ds = 0 m
v0 = (ds – 0.5 sec * a * dt^2)/dt
v0 = (0 m – 0.5 sec * 9.8 m/s/s * 0.5sec^2)/0.5 sec
V0 = 2.45 m/s
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• How high did the ball rise above its point of release before it began to fall back down?
answer/question/discussion: ->->->->->->->->->->->-> :
ds = v0*dt + ½ * a * dt^2
ds = 2.45 m/s * 0.25 sec + ½ * 9.8 m/s/s * 0.25 m/s ^2
ds = 0.919 meters
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17 mins
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No need for revisions but the discussions at the links provided below might be useful.
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Solution
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&#Please compare your 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. &#