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 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: in vertical vf = sort(vo^2 + 2a`ds) = (0+2*9.80*.4) = (7.84) = 2.8m/s, in horizontal vf = sqroot(v0^2 + 2a`ds) = (0+2*9.8*.122) =(2.3912) = 1.55m/s assuming v0 is zero then vAve = 1.55m/s / 2 = .775m/s
The vertical motion is characterized by zero initial velocity and the acceleration of gravity. The .40 cm/s horizontal velocity is not a vertical quantity; the vertical displacement 1.22 m is a vertical quantity, not a horizontal quantity.
The horizontal motion is characterized by zero acceleration.
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: tan-1(1.55/2.8) = 29deg, then 2.8*cos(29) = 2.44, 2.8*sin(29) = 1.36
What are its speed and direction of motion at this instant?
answer/question/discussion: magnitude = sqroot(2.44^2 + 1.36^2) = (7.8032) = 2.79m/s, direction tan-1(2.44/1.36) = 61deg
What is its kinetic energy at this instant?
answer/question/discussion: KE = .5mv^2 = .5*.070kg*2.79^2 = .2724J
What was its kinetic energy as it left the tabletop?
answer/question/discussion: KE = .5mv^2 = .5*.070kg*1.55m/s^2 = .0841J
What is the change in its gravitational potential energy from the tabletop to the floor?
answer/question/discussion: PEgrav = .070kg*9.8m/s^2*.122 = .084J
How are the the initial KE, the final KE and the change in PE related?
answer/question/discussion: since friction or other nonconservative forces are neglected, then the change in KE is equal to -PE
How much of the final KE is in the horizontal direction and how much in the vertical?
answer/question/discussion: KE in horizontal .2724J, KE in vertical is .084J
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30min
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Your overall conception is good; there are some errors in detail.
&#At least part of your solution does not agree with the solution and comments given at the link below. You should view the solution at that link and self-critique as indicated there.
Solution
This link also expands on these topics and alerts you to many of the common errors made by students in the first part of this course. &#