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A uniform smooth sphere P,of mass 3m, is moving in a straight line with speed u on a smooth horizontal table.Another uniform smooth sphere Q, of mass and m and having the same radius as P, moving with speed 2u in the same straight line as P but in the opposite direction to P. The sphere P collides with the sphere Q directly. The velocities of P and Q after the collision are v and w respectively, measured in the direction of motion of P before the collision. The coefficient of restitution between P and Q is e.
a) Find an expression for v in terms of u and e.
b) Show that, if the direction of motion and P is changed by the collision, then e>1/3.
c) Find an expression for w in terms of u and e.
Following the collision with P, the sphere Q then collides with and rebounds from a vertical wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between Q and the wall is e'
Given that e=5/9, and that P and Q collide again in the subsequent motion,
e) Show that e'>1/9
A uniform smooth sphere P,of mass 3m, is moving in a straight line with speed u on a smooth horizontal table.Another uniform smooth sphere Q, of mass and m and having the same radius as P, moving with speed 2u in the same straight line as P but in the opposite direction to P. The sphere P collides with the sphere Q directly. The velocities of P and Q after the collision are v and w respectively, measured in the direction of motion of P before the collision. The coefficient of restitution between P and Q is e.
a) Find an expression for v in terms of u and e.
b) Show that, if the direction of motion and P is changed by the collision, then e>1/3.
c) Find an expression for w in terms of u and e.
Following the collision with P, the sphere Q then collides with and rebounds from a vertical wall which is perpendicular to the direction of motion of Q. The coefficient of restitution between Q and the wall is e'
Given that e=5/9, and that P and Q collide again in the subsequent motion,
e) Show that e'>1/9
