PHYSICS QUESTION

Question

(assuming a perfectly elastic collision), a ball with a mass of 2kg rolls at 2m/s towards a ball with a mass of 3kg rolling at 1m/s in the same direction. The balls collide. After the collision the 2kg ball has a velocity of 0.5m/s. What is the velocity of the 3kg ball?

(assuming a perfectly elastic collision)a ball with a mass of 1kg rolls at 2m/s towards a motionless ball that weighs 2kg. The balls collide, After the collision, the 1kg ball is no longer moving. What is the velocity of the 2kg ball

Answer 1

In a perfectly elastic collision you have conservation of momentum,

which is what both questions are about; they only differ in the numeric values.

Let

m₁ be the mass of ball 1,

m₂ be the mass of ball 2,

v₁ be initial velocity of ball 1,

v₂ be initial velocity of ball 2,

w₁ be final velocity of ball 1,

w₂ be final velocity of ball 2

By conservation of linear momentum,

m₁v₁ + m₂ v₂ = m₁w₁ + m₂ w₂

In general, all the velocities are vectors and the additions are vector additions.

But in both of your examples all the motions are in just one direction,

so we can treat all the velocities as scalars.

In both questions you are to calculate

w2 = (m₁v₁ + m₂ v₂ - m₁w₁)/m₂

Question 1:

m₁ = 2kg,

v₁ = 2m/s,

m₂ = 3kg,

v₂ = 1m/s,

w₁ = 0.5m/s,

w₂ = (2 x 2 + 3 x 1 - 2 x 0.5)/3 = 2m/s

Question 2:

m₁= 1kg,

v₁ = 2m/s,

m₂ = 2kg,

v₂ = 0m/s,

w₁ = 0m/s,

w₂ = (1 x 2 + 2 x 0 - 1 x 0)/2 = 1m/s