Two identical smooth spheres collide. At the instant of collision, the line joining their centres is along the x-axis. Sphere A has velocity (6, 2) m/s and sphere B is initially at rest. The coefficient of restitution is e = 1/2. If the speed of sphere A after collision is N/2 m/s, find N.
Physics · Center of maas , Momentum and Collision · collision and types of collision
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Question

Two identical smooth spheres collide. At the instant of collision, the line joining their centres is along the x-axis. Sphere A has velocity (6, 2) m/s and sphere B is initially at rest. The coefficient of restitution is e = 1/2. If the speed of sphere A after collision is N/2 m/s, find N.

Physics · Center of maas , Momentum and Collision · collision and types of collision

G1 Physics · Accepted Answer

For smooth spheres, collision impulse acts only along the common normal, here the x-axis. Therefore the y-component of velocity of sphere A remains unchanged. Before collision: uAx = 6 m/s, uAy = 2 m/s, uBx = 0. Along x, the masses are equal. Momentum: 6 = vAx + vBx. ...(1) Restitution: vBx − vAx = (1/2)(6) = 3. ...(2) Solving, vAx = 3/2 m/s, vBx = 9/2 m/s. Tangential component of A: vAy = 2 m/s. Hence speed of A: vA = √[(3/2)² + 2²] = √(9/4 + 16/4) = 5/2 m/s. Thus N = 5.