Collision and the phase space

Classical Mechanics Level 2

As shown above, on a frictionless plane, the ball A A whose mass is m m is moving at the velocity v 0 v_0 and collides with the ball B B whose mass is 4 m 4m and velocity is 0 0 .

After the collision, A A moves backwards with the velocity ∣ v ∣ = α v 0 |v|=\alpha v_0 where 0 < α < 1 0<\alpha<1 and has elastic collision with a fixed board P P .

If A A can eventually catch up and collide with B B , how many of the followings would be a appropriate value of α \alpha ?

A. 1 2 \dfrac{1}{2}

B. 2 5 \dfrac{2}{5}

C. 2 3 \dfrac{2}{3}

D. 1 7 \dfrac{1}{7}

4 1 2 3

Alice Smith by Alice Smith , 20, China

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1 solution

Linear momentum conservation equation in the case of first collision between the balls is m v 0 = 4 m v − m α v 0 mv_0=4mv-mαv_0 or v = α + 1 4 v 0 v=\dfrac{α+1}{4}v_0 . Therefore the condition of the problem requires α > α + 1 4 α>\dfrac{α+1}{4} or α > 1 3 α>\dfrac{1}{3} . The two options 2 5 \dfrac{2}{5} and 2 3 \dfrac{2}{3} meet the requirement.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

What about α = 1 2 \alpha = \dfrac{1}{2} ?

Hosam Hajjir - 1 year, 8 months ago

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