Question

deduce the expression for energy loss in one dimensional inelastic collision

Answer 1

The expression for energy loss in A one-dimensional inelastic collision is:

Explanation:

• The two masses m1 and m2.
• m1 is the moving particle with initial speed v1 and m2 is at rest.

• In one-dimensional inelastic collision , Ф1 - Ф2 = 0

• Applying the law of conservation of momentum, we get

                   m1v1 = (m1 + m2) vf  --------- (1)

                   vf = [ m1/m1 + m2 ] v1 ---------(1)

• In this vf is the final velocity of the combined mass (m1+m2)

• The loss in kinetic energy on collision is

           ⇒ΔK = 1/2 M1v1² - 1/2(m1 + m2) vf²

                    = 1/2 m1v1² - 1/2 (m1 + m2 )[ m1/ m1 + m2 * v1²] ---[substituting (1)]

                    = 1/2 m1v1² - 1/2 m1²/ m1 +m2 * v1²

                    = 1/2 m1v1² [ 1 - m1/ m1 + m2]

                     = 1/2 [m1m2/ m1 + m2] v1²

Therefore, the expression for energy loss in one-dimnsional inelastic collision is 1/2 [m1m2/ m1 + m2] v1²