Question

A puck of radius 2R approaches two smaller pucks of radius R at 0.4 m/s along a line between them. It strikes them simultaneously pushing them away at the same angle above and below the original puck direction. The collision causes the large puck to slow to 0.2 m/s. The pucks all have the same thickness and density. a) What is the x-component of the velocity of the smaller pucks after the collision in m/s? b) What is the magnitude of the y-component of the velocity of the smaller pucks after the collision in m/s? Please explain

Answer 1

Mass of smaller pucks = pi*R^2*t *density = m

Then mass of larger puck = pi*(2R)^2*t *density = 4m

Let the x-component of the velocity of the smaller pucks be v

Now by momentum conservation in x axis

initial momentum = final momentum

4m*0.4 = 4m*0.2 + m*v + m*v

1.6 = 0.8 + 2v

v_x = 0.4 m/s answer

b] By conservation of energy,

initial energy = final energy

0.5*4m*0.4^2 = 0.5*4m*0.2^2 + 0.5*m*u^2 + 0.5mu^2

4*0.4^2 = 4*0.2^2 +u^2 + u^2   

2u^2 = 0.64 - 0.16 = 0.48

u = sqrt(0.48/2) = 0.49 m/s

velocity in y direction = sqrt(u^2 - v_x^2) = sqrt(0.24 - 0.4^2)

= 0.283 m/s answer