PHYSICS · Multi-part · CBSE · Physics · Work, Energy and Power · Work, Energy and Power
Problem
Two identical solid spheres, each of mass m, move along the same straight line on a frictionless horizontal surface. Sphere 1 approaches from the left with speed v, while sphere 2 approaches from the right with speed 2v. The spheres collide head-on and rebound without sticking. The coefficient of restitution for the collision is e=0.30 (defined as the ratio of relative speed after the collision to relative speed before the collision).
Ignore external horizontal forces during the brief impact.
(1) Derive algebraic expressions for the speeds of each sphere immediately after the collision in terms of v and e.
(2) Using e=0.30, determine the numerical values of the speeds found in part (a). State the direction of motion for each sphere after the impact.
(3) Calculate the total kinetic energy of the two-sphere system before and after the collision for the case e=0.30.
(4) For an arbitrary value of 0≤e≤1, derive an expression for the fraction of the initial kinetic energy that is dissipated during the collision.
(5) Discuss how the fraction of energy dissipated depends on e, and identify the limiting values that correspond to an elastic collision and to a perfectly inelastic collision for this system.