Work, Power and Energy
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Question : 16
Total: 30
Two identical ball bearings in contact with each other and resting on a frictionless table are hit head-on by another ball bearing of the same mass moving initially with a speed v. If the collision is elastic which of the following figure is a possibleresult after collision?
Solution:
m is the mass of each ball bearing.
Total kinetic energy of the system before collisions
E =
m v 2 + 0 =
m v 2
Kinetic energy of the system after collision
Case I :E =
( 2 m ) × (
) 2 =
m v 2
Case II :E 2 =
m v 2
Case III :E 3 =
( 3 m ) (
) 2 =
m v 2
We observe that kinetic energy is conserved before collision as well as after collision only in Case II. Therefore Case II is the only possibility.
Total kinetic energy of the system before collisions
Kinetic energy of the system after collision
Case I :
Case II :
Case III :
We observe that kinetic energy is conserved before collision as well as after collision only in Case II. Therefore Case II is the only possibility.
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