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PHY 241
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: ->->->->->->->->->->->-> :
The only force acting on the ball during this interval is its 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: ->->->->->->->->->->->-> :
The ball slows down as it moves upwards, reaches it peak with v = 0, and speeds up on its descent. The v-t graph will have a slope equal to constant acceleration due
to gravity. The graph is linear and decreasing for half of the interval, then linear and increasing for the other half with a slope equal and opposite to that during
the first interval.
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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: ->->->->->->->->->->->-> :
Viewed from along teh side of the road, the ball would appear to move as a projectile, slowing down on its way up the arc and speeding up on its way down
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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: ->->->->->->->->->->->-> :
If air resistance is negligible, then the ball will follow the same path as it did in the car ,and if it is not caught it will continue down its parabolic trajectory
until it hits the ground
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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 ball will appear to drop straight down from the child's perspective. The speed will increase at a rate equal to acceleration due to gravity.
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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: ->->->->->->->->->->->-> :
As seen by the child, the ball will appear to drop straight down. As seen by a roadside observer, the ball will move forward at a constant speed as it accelerates
towards the ground, like an object sliding off of a table.
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10 min
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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: ->->->->->->->->->->->-> :
`ds = 10 * .5 = 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: ->->->->->->->->->->->-> :
The ball decelerated upwards to its peak, then accelerated downwards
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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 path observed by people on the roadside would be a concave down parabola, with the ball moving at constant velocity horizontally, decreasing vertical speed on the
first half of the path, increasing vertical speed on the second half
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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: ->->->->->->->->->->->-> :
v_0 = 9.8 * (.5)^2 = 2.45 m/s
2.45 ^2 + 100 = L^2, L = 10.3, `theta = arctan(2.45 / 10) = 14 degrees counterclockwise from x axis
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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: ->->->->->->->->->->->-> :
vAve = 1.23 m/s
`dt = 2.45 / 9.8 = .25 s
`ds = 1.23 * .25 = .31 m
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&#Very good work. Let me know if you have questions. &#