A steel ball bearing of mass 0.056 kg falls to the floor from aheight of 3.2 m.

Question

A steel ball bearing of mass 0.056 kg falls to the floor from aheight of 3.2 m. What is the velocity of the ball bearingimmediately before it hits the ground?  Then the ballbearing rebounds to a height of 3m after striking the floor. Whatis the velocity of the bearing immediately after it leaves thefloor on the rebound? If theball bearimg was in contact with the floor for 0.03 s before itrebounded, determine the impulsive force that the floor exertecd onit while it was in contact with the floor. Note that what isbeing asked for is not the impulse, but the impulsive force!What is the kinetic energyof the ball bearing immediately after it loses contact with theground after the collision? How much potential energy does the ballbearing have when it gets to the maximum height following thecollision with the ground?

Explanation / Answer

A steel ball bearing of mass 0.056 kgfalls to the floor from a height of 3.2 m.
What is the velocity of the ball bearing immediately beforeit hits the ground?  
Ke=Pe
0.5mV2 = mgh
V= (2gh)
V=(2x9.81x3.2)
V= 7.92 m/s
Then the ball bearing rebounds to a height of3m after striking the floor. What is the velocity of the bearingimmediately after it leaves the floor on the rebound?
Still V= (2gh)
Now   h= 3.0m and we have
V=(2x9.81x3)=
V= 7.67 m/s

If theball bearimg was in contact with the floor for 0.03 s before itrebounded, determine the impulsive force that the floor exertecd onit while it was in contact with the floor. Note that what isbeing asked for is not the impulse, but the impulsiveforce!

F=p/t= mv/t=
F= 0.056 x 7.67/0.03=
F=14.3 N

What is the kinetic energy of the ballbearing immediately after it loses contact with the ground afterthe collision?

Ke=0.5mV2
Ke=0.5x0.056 x (7.67)2 Ke=1.65J
How much potential energy does the ballbearing have when it gets to the maximum height following thecollision with the ground? Ke= Pe Pe= 1.65J

Please let me know if you hav eanyproblems.

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