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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.
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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 forces acting on the ball should be that of the mass and gravity. When you initially accelerate in a vehicle you feel a pull, pressing you back against the seat, which if you threw a ball up at this instant, a force would be acted upon the ball, or it would at least seem too. Once you get going things seem to reach an equilibrium between the gravitational forces acting on the car, the force the car exerts on the road, and the force friction exerts against a car allowing it to speed up.
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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 rises with an initial velocity and immediately begins losing kinetic energy to gravitational potential energy until the ball reaches its maximum velocity, at which point all KE will be expended and we will have a stored amount of PE, which will return to us in the form of KE when the ball drops back down. Like I mentioned before, there may be other forces acting on the ball during initial acceleration but those forces seem to level off. Speed vs. clock time should be relative to the acceleration due by gravity. The horizontal velocity of the car could be constant, but regardless of what the horizontal velocity may be, the vertical velocity will be independent of the horizontal velocity. If the car started up an incline we would have to consider the weight component parallel to the incline and how much this effects our acceleration.
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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: ->->->->->->->->->->->-> :
If the car was moving the ball would appear to not only gain vertical direction but it would have to gain horizontal direction also. The horizontal displacement would be proportional to the time the ball spent rising and falling with its vertical velocity. If we multiplied this time by a constant horizontal velocity, say 15m/s for 1s, the ball will have moved horizontally 15m. A passerby would see the car and everything inside it would gain a horizontal displacement, even though most wouldn’t think of it this way, we imagine ourselves stationary while the car moves, but in fact everything the car contains has horizontal velocity and thus will have horizontal displacement. Relative to the road this would affect the landing position of the ball, but if the ball is tossed up in the front seat while the car is moving, the ball does not move to the back seat since everything is moving at a constant velocity. If we speed up significantly while the ball is in the air it will move to the back because the car is moving away from the ball.
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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: ->->->->->->->->->->->-> :
Based on the horizontal velocity of the bicycle and the time the ball is in the air, we can calculate where the ball will land and the magnitude of the displacement if the ball is not caught.
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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: ->->->->->->->->->->->-> :
If a car is moving along at 5m/s and a ball is dropped out of the roof and falls for 3s, the ball will have a horizontal displacement of 15m. If you hold a ball in your hand in a moving vehicle it doesn’t appear to move if the velocity is unchanging, but it makes sense to say that everything in the vehicle has a velocity based on how fast the car is moving.
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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: ->->->->->->->->->->->-> :
Similar effects would occur if the ball was dropped out the window. The child might drop the ball immediately after seeing a white line, he will certainly notice that the ball does not land right where his eye on the white line was, rather it may have landed two white lines in front of where he aimed, since we have a horizontal velocity which will account for some magnitude of horizontal displacement.
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about 15 minutes
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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 have travelled 10m/s * 0.5s = 5m
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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: ->->->->->->->->->->->-> :
From the passenger view, provided he is not scrutinizing the movement of the pavement, he will only see the ball go up and then back down, it will appear not to have any sort of horizontal velocity or show horizontal displacement, but an educated physics students, or someone with just a lot of common sense will know that this is not at all true.
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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: ->->->->->->->->->->->-> :
If five people each with a width of 1 meter are standing in a row with the first person being parallel to the location of the ball as soon as it is released from the childs hand, the 5th person will see the ball come back to the childs hand directly in front of him, while the first person will now be looking at a more rear portion of the car.
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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: ->->->->->->->->->->->-> :
The vertical velocity will appear to be unchanged by the horizontal displacement. If we know at what speed or with what KE the ball ascends and then descends, we can calculate a lot of things for the vertical quantities, but these quantities will act independent of the horizontal quantities.
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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: ->->->->->->->->->->->-> :
The ball will rise 0.25s at which point it will have attained its maximum vertical height and PE, it will be at rest for a moment and After another 0.25 s the ball will have regained its PE in the form of KE and will be safely nestled in the childs hand.
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Very good descriptions. Good thinking throughout.
Do also check the discussion at the link given below. No revision necessary unless you have questions.
&#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
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