Consider an inelastic collision between two objects in one dimension where objec
ID: 1406445 • Letter: C
Question
Consider an inelastic collision between two objects in one dimension where object 2 is stationary, and object 1 has an initial velocity u1 in the initial direction. Object 2 has twice the mass of object 1. After the collision, object 1 has a velocity, V1 = u1/2. What is the velocity of object 2 after the collision, in units of u1? What traction of the energy is lost in the collision, i.e. what energy is lost in units of the initial kinetic energy, Kei? ( The answer will be positive, since the question asks for energy lost.)Explanation / Answer
Un inelastic collision, conservation of momentum occurs.
m1 , u1
m2 = 2*m1 , u2 = 0
after collision velocities becomes:
v1 = u1 /2
applying conservation of momentum:
initial momemtum = final momentum
m1 *u1 = m1 *v1 + m2 *v2
m1 *u1 = m1 *u1 /2 + 2*m1 *v2
u1 = u1 /2 + 2 v2
2* v2 = 0.5 u1
v2 = 0.25 u1 or (1/4) u1
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initial KE of system = 0.5 m1 * u1^2
final ke of system = 0.5 m1 * ()u1 /2)^2 + 0.5 m2 * (v2 )^2
= 0.5 m1 * (u1 /2)^2 + 0.5 *2*m1 * (0.25 u1 )^2
= 0.5 *m1 *()u1)^2 *[1/4 + 1/8] = 0.5 *m1 *(u1)^2 *[0.375]
chnage in ke = final ke - initial ke = 0.5 m1 * u1^2 *[0.375 - 1 ] = -0.625 *[0.5 m1 * u1^2 ]
= -0.625 * ke_i
negative sign shows decrease in ke of system.