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course Phy 121
re-submit
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:
vf^2 = v0^2 + 2 (a)(‘ds)
vf^2 = 0 m/s ^2 + 2 (-9.8 m/s^2)(-1.22 m)
vf^2 = 2 (-9.8 m/s^2)(-1.22 m)
vf^2 = 23.912
vf = 4.9 m/s in the vertical direction.
vf^2 = v0^2 + 2 (a)(‘ds)
(0 m/s)^2 = v0^2 + 2 (9.8 m/s^2)(.4 m)
0 = v0^2 + 7.84 m^2/s^2
v0 = + 2.8 m/s in the horizontal direction
vAve in the horizontal = (0 + 2.8 m/s)/2 = 1.4 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:
vAve in vertical = (4.9 + 0)/2 = 2.45 m/s
vertical components = vx = 2.45 m/s * cos (360) = 0
vy = 2.45 m/s * sin (360) = 2.45 m/s
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• What are its speed and direction of motion at this instant?
answer/question/discussion:
360 degrees
F = ‘sqrt ((0 m/s)^2 + (2.45 m/s)^2)
F= 2.45 m/s
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• What is its kinetic energy at this instant?
answer/question/discussion:
KE = .5 (0.07 kg)(2.45 m/s)^2
KE = 0.21 kg m^2/s^2 or 0.21 N
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• What was its kinetic energy as it left the tabletop?
answer/question/discussion:
KE = .5 (0.07 kg)(1.4 m/s)^2
KE = 0.07 kg m^2/s^2 or 0.07 N
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• What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion:
PE = 0.07 kg * 9.8 m/s^2 * 1.22 m
PE = 0.8 kg m^2/s^2 or 0.8 N
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• How are the initial KE, the final KE and the change in PE related?
answer/question/discussion:
final KE – initial KE = ‘dPE
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• How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion:
In the horizontal, it is 0.07 N and in the vertical, it is 0.21 N
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