Question

Mass 1 is moving at 6 m/s in the +x direction and it collides in a perfectly elastically with mass 2 of 2 kg moving at 15 in the -x direction. They collide for 0.2 seconds, and the average force on mass 1 is 149 N in the -x direction. What is the mass of mass 1 in kg?

Answer 1

Mass of mass 1 = m₁

Mass of mass 2 = m₂ = 2 kg

Initial velocity of mass 1 = V₁ = 6 m/s

Initial velocity of mass 2 = V₂ = -15 m/s (Negative as it is directed along negative X-axis)

Velocity of mass 1 after the collision = V₃

Velocity of mass 2 after the collision = V₄

Average force on mass 1 during the collision = F = -149 N (Negative as it is directed along negative X-axis)

Time period of collision = T = 0.2 sec

Impulse due to the force on mass 1 = I

I = FT

Impulse is equal to the change in momentum of mass 1.

I = m₁V₃ - m₁V₁

FT = m₁(V₃ - V₁)

(-149)(0.2) = m₁(V₃ - 6)

The collision is elastic.

Coefficient of restitution = e = 1

V₄ - V₃ = 21

V₄ = 21 + V₃

By conservation of linear momentum,

m₁V₁ + m₂V₂ = m₁V₃ + m₂V₄

m₁ = 1.1 kg

Mass of mass 1 = 1.1 kg