Calculating Linear Momentum in Elastic Collision of Two Balls

[Lorentz]

Two balls hit each other.

One ball with a mass of 2m standing still relative to the earth. The other ball has a mass of 1m and hits the ball of 2m at a certain speed. The collision is elastic.

Could you calculate the proportion of Linear Momentum between both balls after the collision with this information?

 

[Chen]

M₁ = 2m
M₂ = m
v - speed before collision
u - speed after collision

$$M_1v_1 + M_2v_2 = M_1u_1 + M_2u_2$$

Cancelling the mass and zero speed we get:

$$v_2 = 2u_1 + u_2$$

Second equation:

$$\frac{1}{2}(M_1v_1^2 + M_2v_2^2) = \frac{1}{2}(M_1u_1^2 + M_2u_2^2)$$

Cancelling the mass and zero speed we get:

$$v_2^2 = 2u_1^2 + u_2^2$$

Two equations with two variables, you can find both u₁ and u₂ and therefore the ratio of linear momentums of both balls. I think it turns out to be -1...

(By the way, I assumed head-on collision here. If it's not you also need the angle.)

 

[Lorentz]

(By the way, I assumed head-on collision here. If it's not you also need the angle.)

Thanks!... it's actually not a head-on collision, but I figured out I could manage to fit in the angle myself. If I experience difficulties I'll let you know.