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Phy 201
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** CQ_1_22.2_labelMessages **
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^2, ds=122 cm
vf=sqrt(0 cm/s)^2+2(980 cm/s^2)*122 cm=489 cm/s
dt=(489 cm/s)/(980 cm/s^2)=.5 s
Horizontal motion=ds/dt=40 cm/.5 s=80 cm/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: ->->->->->->->->->->->-> :
x component=80 cm/s
y component=-489 cm/s
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What are its speed and direction of motion at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
magnitude=sqrt(80 cm/s)^2+(489 cm/s)^2=495.5 cm/s
angle=arctan(-490 cm/s^2/80 cm/s^2)=-81 degrees
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What is its kinetic energy at this instant?
answer/question/discussion: ->->->->->->->->->->->-> :
KE=1/2mv^2=1/2(.07 kg)(4.96 m/s)^2=.86 J
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What was its kinetic energy as it left the tabletop?
answer/question/discussion: ->->->->->->->->->->->-> :
IT was moving at 80 cm/s or .8 m/s as it was leaving the tabletop so,
KE+=1/2(.07 kg)*(.8 m/s)^2=.02 J
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What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: ->->->->->->->->->->->-> :
dKE=.86 J-.02 J=.84 J, so dPE=-.84 J
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How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: ->->->->->->->->->->->-> :
dKE+dPE=0
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How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: ->->->->->->->->->->->-> :
0.0224 J is in the horizontal, because there was no velocity change horizontally, which gives a KE final and initial being the same in the horizontal direction. The vertical direction has the remaining 0.8387 J, which it gained as a conversion of PE to KE during the drop.
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