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: ->->->->->->->->->->->-> :
vertical:
v0 = 0 cm/s
a = 980 cm/s/s
ds = 122 cm
vf^2 = v0^2 + 2 * a * ds
vf ^2 = (0 cm/s)^2 + 2 * 980 cm/s/s * 122 cm
vf = +-489 cm/s
vf = v0 + a * dt
489 cm/s = 0 cm/s + 980 cm/s/s * dt
dt = 0.5 sec
horizontal:
vAve = ds/dt
vAve = 40 cm/0.5 sec
vAve = 80 cm/sec
#$&*
• Assuming zero acceleration in the horizontal direction, what are the vertical and horizontal components of its velocity the instant before striking the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
x component: 80 cm/sec
y component: -489 cm/sec
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• What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
magnitude = sqrt( 80^2 + -489^2)
magnitude = 495.5 cm/s
direction = tan-1(-489 / 80) = -80.7 degrees
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• What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
KE = ½ * m * v^2
489 cm/s = 4.89 m/s
70 g = 0.07 kg
KE = ½ * 0.07 kg * (4.89 m/s)^2
KE = 0.84 J
the ball is moving at 4.95 m/s, not 4.89 m/s
#$&*
• What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
KE = ½ * m * v^2
80 cm/sec = 0.8 cm/sec
KE = ½ * 0.07 kg * (0.8 m/s)^2
KE = 0.022 J
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• What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
U = mgh
U = 0.07 kg * 9.8 m/s/s * (1.22 m – 0 m)
U = 0.84 J
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• How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: ->->->->->->->->->->->-> :
final KE = initial KE + 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: ->->->->->->->->->->->-> :
KE = 0.84 J
KE = 0.022 J
as found previously
#$&*
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25 mins
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Your energy conservation doesn't quite work out. As long as you understand everything at the link, no revision is necessary.
&#Please compare your solutions with the expanded discussion at the link
Solution
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