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PHY 231
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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: ->->->->->->->->->->->-> :
ds = v0*dt + .5*a*dt^2
1.22m = (.5)(9.8m/s^2)(dt)^2
dt=.5s,
vf^2 = 2*9.8m/s^2*1.22m
vf = 4.9m/s
vAve_H =.4m/.5s = .8 m/s
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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: ->->->->->->->->->->->-> :
-.8m/s and -4.9 m/s
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• What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
x^2 = (-.8m/s)^2 + (-4.9m/s)^2
x = 4.96 m/s
Direction
tan^-1((-4.9m/s)/-.8m/s) = 81 deg off the x axis (downward to the left)
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• What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
KE = .5(.07kg)(-4.96m/s)^2
KE = .861J
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• What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
KE = .5(.07kg)(.8m/s)^2
KE = .0224J
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• What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
dPe = .861J - .0224
dPE = -.8386J
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• How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: ->->->->->->->->->->->-> :
The difference in the initial KE and final KE should be equal to the change in PE * -1 due to the law of conservation.
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• How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: ->->->->->->->->->->->-> :
.0224J horizontally
Vertically = .861-.0224J
Vertically = .8386J
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Another 10 min or so...maybe less.
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#$&* self-critique
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