- #1

ChrisBrandsborg

- 120

- 1

## Homework Statement

A hockey puck of mass M hits two other, identical pucks of mass m. The two pucks fly off with the same speed vf at angles of ±θ relative to the direction the original puck was traveling (see figure). The original puck had initial speed vi, and the two other pucks were initially at rest. We will assume that the pucks are sliding frictionlessly on the ice.

a) If the collision is elastic and the first puck ends up at rest after the collision, what is the final speed vf of the two other pucks and the angle θ?

b) What relation must one require between m and M in order for the scenario of a) to be possible? What happens if this requirement on m and M is not met?

For each question, provide an algebraic expression in terms of (some or all of) M, m, vi.

## Homework Equations

E

_{k}: 1/2mv

_{i}

^{2}= 1/2mv

_{f}

^{2}

## The Attempt at a Solution

a) E

_{k}conserved:

1/2Mv

_{i}

^{2}= 2(1/2mv

_{f}

^{2})

v

_{f}= √(Mv

_{i})

^{2}/2m

How do I find the angle?

Px = 0 -> 0 = 2mv

_{f}⋅sinθ

Py = 0 -> Mv

_{i}= 2mv

_{f}⋅cosθ

I know the angle should be 45°, but can't figure out exactly how to get there.

b) 1/2Mv

_{i}= 2(1/2mv

_{f})

Make an equation for M:

M = 2m (v

_{f}

^{2}/v

_{i}

^{2})

Which means that if this requirement isn't met, than its not elastic and K is not conserved.

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