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phy 231
Your 'cq_1_13.1' 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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Seed Question 13.1
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?
When gravity is the only force acting on the free falling object, horizontal and vertical motions are completely independent of each other.
Vertically, gravity is accelerating the ball, therefore a = 9.8 m/s/s or 980 cm/s/s
`ds = 120 cm below and v0 = 20 cm/s
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• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
vf^2 = v0^2 + 2*a*`ds,
vf = sqrt ( (20 cm/s)^2 + 2 * 980 cm/s/s*120 cm) = 485.4 cm/s
`ds = 120 cm
`dv = (485.4 cm/s - 20 cm/s) = 465.4 cm/s
vAve = (485.39 cm/s + 20 cm/s)/2 = 252.7 cm/s
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• What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
The ball’s acceleration in the horizontal direction is constant, a = 0.
v0 horizontal = 80 cm/s
The clocktime is the same horizontally as it is vertically:
`dt = `ds/(vf - v0)/2 = 120 cm/(485.39 cm/s - 20 cm/s)/2 = .52 sec
@& `dt = `ds / vAve, not `ds / `dv.*@
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• What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
`ds horizontal = 80 cm/s * .52 sec = 41.6 cm
vf = 80 cm/s, vAve = 80 cm/s, `dv = 0 cm/s
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• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
Depending on the material of the ball, if it’s elastic and bounces it may accelerate. Otherwise, the ball may just hit and basically stop.
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• Why does this analysis stop at the instant of impact with the floor?
Because we don’t know the material of the ball and any other information about the impact.
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30 min
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July 21st, 12:14 pm
@& You had one error. Be sure you understand.
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Solution
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