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Phy 231
Your 'cq_1_22.2' 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 70 gram ball rolls off the edge of a table and falls freely to the floor 122 cm below. While in free fall it moves 40 cm in the horizontal direction. At the instant it leaves the edge it is moving only in the horizontal direction. In the vertical direction, at this instant it is moving neither up nor down so its vertical velocity is zero. For the interval of free fall:
• What are its final velocity in the vertical direction and its average velocity in the horizontal direction?
answer/question/discussion: ->->->->->->->->->->->-> :
final velocity in vert direction= 489cm/s found by vf= sqrt(2a*ds) which is vf= sqrt(2*980cm/s^2*122cm)= 489cm/s
dt= sqrt((2ds)/a) which is sqrt((2*122cm)/980cm/s^2)= .5s
40cm/.5s= 80cm/s= v0
vAve= 80cm/s/2= 40cm/s
@& The ball doesn't change speed in the horizontal direction. vAve = vf / 2 when acceleration is uniform and initial velocity is zero; that doesn't apply here. Besides which 80 cm/s is the average velocity, not the initial and not the final velocity (both of which are equal to the average velocity in this case).*@
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• Assuming zero acceleration in the horizontal direction, what are the vertical and horizontal components of its velocity the instant before striking the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
hor comp= 80cm/s, vert comp= 489cm/s
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• What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
arctan(vy/vx)= arctan(489cm/s/80cm/s)= 80.7degrees
speed is sqrt((489cm/s)^2 + (80cm/s)^2)= 495.5cm/s
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• What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
KE= ½ mv^2= ½ (.07kg)(.4955m/s)^2=.0086Joules
@& Good, but 495.5 cm/s is 4.95 m/s, not .4955 m/s. So the KE is 100 times what you have reported.*@
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• What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
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• What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
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• How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: ->->->->->->->->->->->-> :
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• How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: ->->->->->->->->->->->-> :
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30min
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Solution
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