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PHY 201
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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SEED Question 22.2
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: ->->->->->->->->->->->-> :
Given:
mass = 70 kg; ds (vert) = 122 cm or 1.22 m; ds (horiz) = 40 cm or .40 m; v0 = ?; vf = ?; vAve (horiz) = ?
vf^2 = v0^2 - 2 * g * ds
vf^2 = -2 * g * ds
vf^2 = -2 * -9.8 m/s^2 * 1.22 m
vf^2 = 23.9 m^2/s^2
vf = sqrt 23.9 m^2/s^2
vf = 4.9 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: ->->->->->->->->->->->-> :
vf = v0 + a * dt
vf = a * dt
dt = vf / a
dt = 4.9 m/s / 9.8 m/s^2
dt = 0.5 s
vAve (horiz) = ds / dt
vAve (horiz) = .04 m / 0.5 s
vAve (horiz) = 0.8 m/s
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• What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
c^2 = a^2 + b^2
c^2 = 4.9^2 + 0.8^2
c^2 = 24.01 + 0.64
c^2 = 24.7
c = sqrt (24.7)
c = 5.0 m/s
sin (theta) = opp / hyp
sin (theta) = (4.9 / 5.0)
sin (theta) = 0.98
theta = sin ^-1 (0.98)
theta = 78.5 deg
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• What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
KEf = ½ mv^2
KEf = ½ * .070 kg * 5.0^2 m/s
KEf = 0.86 J
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• What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
KE0 = ½ mv^2
KE0= ½ * .070 kg * 0.8^2 m/s
KE0 = 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: ->->->->->->->->->->->-> :
PE = mgh
PE = 0.070 kg * 9.8 m/s^2 * 1.22 m
PE = 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 = dPE = 0.86 J - 0.022 J = 0.84 J
dPE + Initial KE = Final KE = 0.84 J + 0.022 J = 0.86 J
Final KE - dPE = Initial KE = 0.86 J - 0.84 J = 0.022 J
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• How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: ->->->->->->->->->->->-> :
25% of the final velocity is in the vertical direction and 75% is in the horizontal direction.
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30 mins
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SEED Question 22.2 was submitted 23 Mar 2011 around 10:42 PM.
&#Good responses. Let me know if you have questions. &#