Question #106029

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.

Expert's answer

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"

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Olisah kenneth12.04.22, 17:50Awesome, thanks

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