Phy 121
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A ball rolls off the end of an incline with a vertical velocity of 20 cm/s downward, and a horizontal velocity of 80 cm/s. The ball falls freely to the floor 120 cm below.
• For the interval between the end of the ramp and the floor, what are the ball's initial velocity, displacement and acceleration in the vertical direction?
The initial velocity would be 20cm/s. We know that the object travels 120 cm as it falls in the vertical direction. This is our total displacement.
To find the time period I took my displacement and divided it by my average velocity. This gave me a time period of 12s. ( I know that by the math it would be a negative number, but since time can’t be negative I left it as positive….perhaps I should have declared which direction on my ramp was positive or negative beforehand?)
So to find acceleration, I took the change in velocity, which was -20m/s and divided it by my time period of 12s. This gave me an acceleration of -1.6 cm/s^2.
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• What therefore are its final velocity, displacement, change in velocity and average velocity in the vertical direction?
Final velocity is 0
The final velocity is the last velocity attained during the uniform downward acceleration. When the ball comes into contact with the floor, the net force on it changes so acceleration changes. The uniform-acceleration interval has therefore ended and our uniform-acceleration analysis becomes invalid.
Displacement is 120 cm
Our change in velocity would then be -20 m/s. To find my average velocity I took vf+ v0 and divided by 2. This gave me a total of -10m/s as my average velocity.
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• What are the ball's acceleration and initial velocity in the horizontal direction, and what is the change in clock time, during this interval?
Acceleration is -6.6cm/s^2. I found this by taking my average velocity of -40cm/s and dividing it by the time interval of 12 s.
The initial velocity is 80cm/s.
The change in clock time is 12seconds.
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• What therefore are its displacement, final velocity, average velocity and change in velocity in the horizontal direction during this interval?
The displacement of the object is 480m.
The final velocity is 0.
The change in velocity is -80cm/s.
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• After the instant of impact with the floor, can we expect that the ball will be uniformly accelerated?
I think that while the ball is accelerating that it will do so uniformly, but once it stops that it will no longer be accelerating uniformly. The ball should stop for an instant, but may then roll off in a direction until it stops. This motion would not be uniform.
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• Why does this analysis stop at the instant of impact with the floor?
This analysis stops at the instant of impact with the floor because the object (ball) is now at rest.
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45 minutes
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Solution
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