Change In Momentum With No Loss Of Ke

[studentmom]

Homework Statement

A ball with original momentum of +4.0 kg*m/s hits a wall and bounces straight back without losing any kinetic energy. The change in momentum of the ball is?

Homework Equations

p (momentum) = mv
Impulse = change in p/change in t

The Attempt at a Solution

I thought that if the KE was conserved, then momentum had to be conserved to, so needless to say, I am confused. Any help would be appreciated!

 

[studentmom]

just bumping up ... any ideas??

 

[OlderDan]

You are correct that momentum is conserved. In fact, it is conserved even if the energy is not. Every collision involves more than one object. In this case there are two objects. Conservation of momentum means that the sum of the momenta of the two objects is conserved, not that the momentum of a single object is conserved.

If you look at the definitions of momentum and kinetic energy you will see that an object can acquire momentum while gaining almost no kinetic energy. (How can this be?) Strictly speaking the ball cannot retain all of its energy when bouncing off the wall, but the amount that it must lose is such a small fraction of what it had to begin with that for all practical purposes it has not lost any.

 

[jtbell]

Hint: Momentum is a vector. Momentum can change by changing either the magnitude or the direction, or both. If the momentum changes from (just for example) 10 kg-m/sec to the left to 10 kg-m/sec to the right, what is the change in momentum?