Moving in a curved surface
Object
with a mass of
is about to slide down a curved surface from the height of
to collide with object
at the bottom with a mass of
as shown above. If the coefficient of restitution between the two objects is
then what is the speed of object
immediately after the collision? (Ignore air resistance, all frictional forces and the sizes of the objects.
denotes gravitational acceleration.)
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1 solution
Looking just at Object A, the velocity of the object after moving down a distance of h is sqrt(2gh). Then, using conservation of momentum, m 2 g h = m v A , a f t e r + 2 m v B , a f t e r . and another equation (not from conservation of momentum) can be created too: v B , a f t e r − v A , a f t e r = 0 . 5 2 g h . Then, one can solve for v A , a f t e r in the second equation and substitute it into the first. From there, one can solve for v B , a f t e r , which comes out to be 2 g h