final velocity question- physics. please help :)

Question

Two marbles with equal masses collide. Marble A has an initial velocity of 2.37 m/s while marble B is initially at rest. If marble A comes to rest as a result of the initial collision, what is the final velocity of marble B?

 

also, what kind of collision is this? Perfectly Inelastic, Inelastic but not perfectly inelastic, or Elastic?

 

thank you! :)

Answer 1

Use conservation of linear momentum.

 

m = mass of the two marbles

v₁ = initial velocity of marble A = 2.37 m/s

v₂ = final velocity of marble A = 0

u₁ = initial velocity of marble B = 0

u₂ = final velocity of marble B = ?

 

Assume initial direction of marble A is positive.

 

mv₁ + mu₁ = mv₂ + mu₂ ⇒

 

v₁ + u₁ = v₂ + u₂ ⇒

 

u₂ = v₁ + u₁ - v₂ = (2.37 + 0 - 0) = 2.37 m/s

 

Note that the total kinetic energy before and after is the same, so the collision is elastic.

 

K_i = mv₁²/2 

K_f = mu₂²/2 

 

But in this problem, v₁ = u₂, so K_i = K_f