Mass m1 moving at constant velocity v1 along the x axis collides with mass m2 in
ID: 2259513 • Letter: M
Question
Mass m1 moving at constant velocity v1 along the x axis collides with mass m2 initially at rest. Assume that the two masses continue to move along the x axis after the collision.
1. Determine the final velocities of the two masses if their collision is perfectly inelastic. Derive using any applicable conservation laws.
2. Determine the final velocities of the two masses if their collision is perfectly elastic. Derive using any applicable conservation laws.
Explanation / Answer
1). the bodies will stick after collision. from momentum conservation; m1*v1 = (m1 +m2)*v => v = (m1*v1)/(m1+ m2) 2). let the velocity of mass m1 after collision be v2 and that of mass m2 be v3. K.E. of the system is conserved after collision. from K.E. conservation; 0.5*m1*v1^2 = 0.5*m1*v2^2 + 0.5*m2*v3^2 from momentum conservation; m1*v1 = m1*v2 + m2*v3 from the above two equations; v2 = v1 - [(2*m2^2*v1)/(m2^2 +m1*m2)] v3 = (2*m1*m2*v1)/(m2^2 +m1*m2)