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Phy 121
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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 infree 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: ->->->->->->->->->->->-> :
The final velocity in the vertical direction is as follows:
vf^2 = v0^2 + 2*a*’ds
vf^2 = (0m/s)^2 + 2*9.8m/s^2*1.22m
vf^2 = 23.9m^2/s^2
vf = +-4.9m/s (In this case positive)
vf = v0+a*’dt
4.9m/s = 0m/s + 9.8m/s^2*’dt
4.9m/s = 9.8m/s^2*’dt
.5s = ‘dt
The horizontal average velocity is as follows:
.04m/.5s = .08m/s
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40 cm is .40 m, not .04 m, so the displacement is .80 m, or 80 cm.
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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: ->->->->->->->->->->->-> :
The vertical component is 4.9m/s and the horizontal component is .08m/s.
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• What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
The speed is as follows:
c^2 = (.08m/s)^2 + (4.9m/s)^2
c^2 = 24.0164m^2/s^2
c = 4.9m/s
The direction is as follows:
Tan^-1(4.9/.08) = 89.1 degrees in relation to the positive x axis.
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• What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
The KE is as follows:
KE = ½*m*v^2
KE = ½*.07kg*(4.9m/s)^2
KE = .84035J
KE = ½*m*v^2
KE = ½*.07kg*(.08m/s)^2
KE = .000224J
Therefore the total KE is .840574J
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• What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
The KE is as follows:
KE = ½*m*v^2
KE = ½*.07kg*.08m/s^2
KE = .000242J
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• What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
The change in the gravitational potential energy is -.840332J because that is the amount the KE increased.
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• How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: ->->->->->->->->->->->-> :
The change in KE is equal and opposite to the change in PE.
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• How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: ->->->->->->->->->->->-> :
.000242J of the final KE is horizontal and .84035 of the final KE is vertical.
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20 minutes
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Very good. Everything you're doing is right, though you did base your results on a horizontal velocity of 4 cm/s rather than 40 cm/s.
Check my note.
The following is for your reference only:
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