phy 201
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A ball rolls off the end of an incline with a vertical velocity of 20 cm/s downward, and a horizontal velocity of 80 cm/s. The ball falls freely to the floor 120 cm below.
• For the interval between the end of the ramp and the floor, what are the ball's initial velocity, displacement and acceleration in the vertical direction?
• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
• What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
• What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
• Why does this analysis stop at the instant of impact with the floor?
1) The initial velocity would be 20 cm/s downward, which is given; the displacement is given, 120 cm in the vertical direction; and the acceleration in the vertical direction over the time period is (A = (vf-v0)/(‘ds/vAve) = 20 / 12 = 1.67 cm/s/s).
2) The final velocity of the ball in the vertical direction is 0 cm/s since we assume the ball will come to rest at the point at which it makes contact with the floor; the displacement is 120 cm in the vertical direction, which is given; the change in velocity is therefore (20 cm/s - 0 cm/s = 20 cm/s) from initial to final; and the average velocity over the 120 cm in the vertical direction is ( (0 cm/s + 20 cm/s) / 2 = 10 cm/s).
3) Since the time interval will be the same in the horizontal as that of the vertical, we can place a value of 12 seconds in the ratio. Therefore, (80 / 12 = 6.67 cm/s/s); the initial velocity is given to be 80 cm/s.
4) The displacement in the horizontal direction can be found by (vAve = ‘ds/’dt ‘ds = vAve * ‘dt = 40 * 12 = 480 cm); the final velocity is also 0 cm/s since we would take the interval from the end of the ramp to the point it touches the floor; the average velocity is simply ( (80 + 0)/2 = 40 cm/s); so therefore the change in velocity is (80 – 0 = 80 cm/s).
5) Yes we can expect it to be, as long as no unexpected force acts on the object to change its magnitude or direction of velocity.
6) It stops with the instant of impact because there is no information on what the ball is made of, what the floor is made of, and what the force of gravity is for the given situation.
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20 minutes
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&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
This link also expands on these topics and alerts you to many of the common errors made by students in the first part of this course. &#