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Inelastic collision & gradient of potential energy

See attached file.


Solution Preview

Gradient problems are in the attachments.

Collision problem:

Conservation of momentum:

m1 v1 = (m1 + m2)v2 ------->

v2 = m1v1/(m1 + m2)

Kinetic energy after collision:

1/2 (m1 + m2)v2^2 = 1/2 m1^2 v1^2/(m1 + m2)

Kinetic energy has decreased by:

1/2 m1 v1^2 - 1/2 m1^2 v1^2/(m1 + m2)

Divide by 1/2 m1 v1^2 to find the relative fraction that has been lost:

[1/2 m1 v1^2 - ...

Solution Summary

A problem about inelastic collsion is solved and we consider an unrelated problem on gradients of potential energy functions.