Question

A mass 1.9 kg is initially at rest at the top of a 2meter high ramp. It slides down the frictionless ramp and collides elastically with an unknown mass which is initially at rest. After colliding with the unknown mass, the 1.9 kg mass recoils and achieves a maximum height (altitude) of only 0.2 m going back up the frictionless ramp. (HINT: Solving each part in sequence will guide you to a solution without doing a lot of algebra.)

1.Considering the energy of the 1.9 kg mass just before and just after the elastic collision, how much energy is lost by the 1.9 kg mass?

2.What is the speed of the 1.9 kg mass just before the elastic collision?

3.What is the speed of the 1.9 kg mass just after the elastic collision?

4.Considering conservation of momentum, what is the momentum of the unknown mass just after the elastic collision?

5.What is the kinetic energy of the unknown mass after the elastic collision?

6.What is the velocity of the unknown mass just after the elastic collision?

7.What is the mass of the unknown mass in kg?

Answer 1

Given,

m1 = 1.9 kg ; h = 2 m ; h' = 0.2 m

1)Intial energy of the m1

Ei = m g h

Ei = 1.9 x 9.81 x 2 = 37.28 J

Ef = m g h'

Ef = 1.9 x 9.81 x 0.2 = 3.728 J

Energy lost will be:

E(lost) = 3.728 - 37.28 = -33.552 J

Hence, E(lost) = -33.552 J

2)PE gets converted to KE

1/2 m v^2 = m g h

v = sqrt (2gh) = sqrt(2 x 9.81 x 2) = 6.26 m/s

Hence, vi = 6.26 m/s

3)Energy is lost in collision is, m1 is left with

Ef = 3.728

vf = sqrt (2 x 3.728/1.9) = 1.98 m/s

Hence, vf = 1.98 m/s

4)From conservation of momentum

m1vi + m2v2 = m1vf + P2

1.9 x 6.26 + 0 = 1.9 x 1.98 + P2

P2 = 8.132 kg-m/s