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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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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, hat are the ball's initial velocity, displacement and acceleration in the vertical direction?
Vert. v0=20cm/s
ds= 120cm
a= 980cm/s^2
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• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
vf= sqrt ((20cm/s)^2 + 2(980cm/s^2)(120cm))
vf= sqrt (235600cm^2/s^2)= 485.4cm/s
ds= 120cm
dv= (485.4cm/s) - (20cm/s)= 465.4cm/s
vAve= (485.4cm/s + 20cm/s)/2= 252.7cm/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?
dt= ds/vAVe= 120cm/(252.7cm/s)= .475s
v0= 80cm/s
ds= 80cm/s * .475s= 38cm
a= (80cm/s - 0)/.475s= 168.4cm/s^2
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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= 38cm
vf= 0cm/s
vAve= 40cm/s
dv= -80cm/s
@& If vAve was 40 cm/s then the ball would only have traveled 19 cm in the horizontal direction.
During the uniform acceleration from the instant the ball leaves the ramp to the instant it hits the floor, there is no significant force in the horizontal direction, so there is no significant acceleraiton in that direction. Therefore velocity remains constant, and `dv = 0.*@
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• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
Yes, because when it impacts the floor the ball will just have horizontal acceleration that is decreasing as time goes on, if the floor is not sloped.
@& The acceleration of the ball is in the vertical direction, and certainly changes when the ball hits the floor.
If the ball dents the floor, of if there is friction between the ball and the floor, it will also experience a change in horizontal acceleration.*@
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• Why does this analysis stop at the instant of impact with the floor?
Because of the many uncertainties when the ball hits the floor. The ball could bounce when it hits the floor, friction from the ball rolling across the floor, and that the vertical velocity is 0 when it hits the floor.
@& The analysis assumes uniform acceleration, which is no longer the case when the ball contacts the floor.*@
&#Your work looks good. See my notes. Let me know if you have any questions. &#