Fraction of K.E. that turned into P.E.

Gold Member

Homework Statement

A ball moving translationally collides elastically with another, stationary, ball of the same mass. At the moment of impact the angle between the straight line passing through the centres of the balls and the direction of the initial motion of the striking ball is equal to α = 45° Assuming the balls to be smooth, find the fraction of the kinetic energy of the striking ball that turned into potential energy at the moment of the maximum deformation.

Homework Equations

Conservation of momentum
Energy Conservation Principle

The Attempt at a Solution

I don't understand what will happen at the time of max deformation. I mean to say that what will be the velocities of the particle at that instant. I can apply conservation of momentum but that will lead me to nowhere. Also applying conservation of energy I can know what will be the final velocities but not the velocities at the time of max deformation. So what should I use?

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NascentOxygen
Staff Emeritus
The line of thought is probably that all of the KE acquired by the second ball comes from elastic deformation during the interaction.

Gold Member
The line of thought is probably that all of the KE acquired by the second ball comes from elastic deformation during the interaction.
So how should I proceed? What equations will I have to apply?

NascentOxygen
Staff Emeritus
Determine the KE acquired by ball #2.

Gold Member
Determine the KE acquired by ball #2.
Oh now I think how easy it was. Thanks for helping. :tongue:

NascentOxygen
Staff Emeritus
A further thought....the question concerns "the kinetic energy of the striking ball that turned into potential" elastic energy, so I think you should find the K.E. of ball #2 and double it. Why double it? From Newton's 3rd Law (his action-reaction law), it follows that after the point of maximum elastic deformation, while one ball receives a certain energy in one direction, the other receives the same in the opposite direction. (It's an elastic collision, so energy is conserved.)

Gold Member
A further thought....the question concerns "the kinetic energy of the striking ball that turned into potential" elastic energy, so I think you should find the K.E. of ball #2 and double it. Why double it? From Newton's 3rd Law (his action-reaction law), it follows that after the point of maximum elastic deformation, while one ball receives a certain energy in one direction, the other receives the same in the opposite direction. (It's an elastic collision, so energy is conserved.)
But I got my answer without doubling it.