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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.
Gravity, the forward force of the car
The gravitational force exerted by the Earth on the ball, i.e., the weight of the ball, will act at all times.
During the interval between release and catch, the child's hand is not in contact with the ball and cannot exert a force on it.
During the interval between release and catch, the automobile is not in contact with the ball and cannot exert any force on it by means of contact.
Other than negligible air resistance, and the even more negligible gravitational interaction between the car and the ball, the only force acting on the ball is its weight.
• 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.
The speed of the ball would be high upon release, slowing down as it reaches its apex, the regaining speed on the return trip. I’m thinking the graph would be a positive parabola. from t=0, speed would be high, gradually declining and then gradually increasing until t=time it returned to hand
As the ball rises to its apex its speed will decrease at a constant rate with respect to clock time. As it then falls its speed increases with respect to clock time, again at a constant rate. The speed vs. clock time graph therefore consists of two straight-line segments, forming a V.
• Describe the path of the ball as it would be observed by someone standing along the side of the road.
I believe it would appear to go straight up and straight back down to someone on the side of the road.
As observed from the side of the road the ball travels forward at constant speed as it rises then falls.
The ball changes speed in the vertical direction but not in the horizontal.
The path is therefore curved--in fact it can be shown that the path is parabolic.
• 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).
The path of the ball would not be straight up and down, due to the force of wind on the ball.
• 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).
The speed will increase due to gravity. the acceleration will be 9.8m/s^2.
• 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).
The ball looks as though it is falling down and away from the child. To observers, the ball looks as though it falls forward, in the direction of the car.
The ball is observed from the roadside to speed up in the vertical direction but not in the horizontal, causing the path to curve (as it turns out the path is in fact parabolic).
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8 mins
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