Question

Two shuffleboard disks of equal mass, one orange and the other green, are involved in a perfectly elastic glancing collision. The green disk is initially at rest and is struck by the orange disk moving initially to the right at 5.00 m/s as in Figure P6.40a. After the collision, the orange disk moves in a direction that makes an angle of 37.0° with the horizontal axis while the green disk makes an angle of 53.0° with this axis as in Figure P6.40b. Determine the speed of each disk after the collision.

Answer 1

It is case of elastic collision.

We have to apply the momentum conservation equation for both horizontal a d vertical direction.

$(sin \ 37 \degree=cos\ 53\degree=\frac{3}{5};sin\ 53\degree=cos \ 37\degree=\frac{4}{5})$

Let the velocity of green ball be $v_g$ and that of orange is $v_o.$

Applying momentum conservation in horizontal axis,

$5=v_o cos\ 37\degree+v_gcos \ 53\degree$

$\implies 4v_o+3v_g=25\ \ \ (1)$

Applying momentum conservation in vertical direction,

$0=v_osin\ 37\degree-v_gsin \ 53\degree$

$\implies v_o=\frac{4}{3}v_g$

Substituting this in $(1),$

$4\times \frac{4}{3}v_g+3v_g=25$

$\implies v_g=3\ m/sec$

$\implies v_o=\frac{4}{3}v_g=\frac{4}{3}\times 3=4\ m/sec$