If an object is mass m with a velocity u collides with a stationary object of mass m, how much kinetic energy is lost?

Answer 1

There will be no loss of kinetic if the collision is elastic and in all cases momentum will be conserved. If the collision is inelastic some energy is converted to heat.

When two objects collide, their kinetic energy is conserved unless part of the energy was transformed into a different form during the collision. In the event of an inelastic collision, some energy is transformed into heat but momentum is conserved. This is because energy is always conserved.

So, before the collision a mass #m# has velocity #u#. It hits another object of mass #m# which is at rest. After the collision the combined bodies have mass #2m# and velocity #v#. Now momentum is conserved so:

#m u=2m v#

This means that #v=u/2# and momentum is conserved.

The kinetic energy has changed to:

#1/2 m u^2 - 1/2 2m v^2 = 1/2m u^2 - m u^2/4=1/4 m u^2#

So, the loss of kinetic energy is #1/4m u^2#.

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Answer 2

Layla Ahmed

The kinetic energy lost in the collision is ( \frac{1}{2}m(u^2) ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.