Question

a)A 5.00kg moving object with a velocity of 2.00 m/s has a head-on elastic collision (angle = 180^o) with a 10.0 kg of object that is not moving. What would be the final velocity of the 5.00kg object?

b)A 5.00kg moving object with a velocity of 2.00 m/s has a head-on inelastic collision (angle = 180^o) with a 10.0 kg of object that is not moving. What would be the final velocity of the 5.00kg object?

Answer 1

a) let the final velocity of 5 kg object be v1 and 10 kg object be v2

By the conservation of momentum we have

m1u1 + m2u2 = m1v1 + m2v2

5*2 + 10*0 = 5v1 + 10v2

v1 + 2v2 = 2 ------------(1)

velocity of approach = velocity of recess

v2 - v1 = u1 - u2

v2 - v1 = 2 - 0

v2 - v1 = 2 -------(2)

Multiply (2) by 2 and subtracting from (1) we have

3v1 = --2

v1 = -2/3 m/s

so speed of 5 kg after collision is 2/3 m/s in the opposite direction

b) Since the collision is elastic , the final velocity will be V m/s

By the conservation of momentum we have

m1u1 + m2u2 = (m1 + m2)*V

5*2 + 10*0 = (5 + 10)*V

V = 2/3 m/s

so speed will be 0.67 m/s in the same direction