Dynamics_Part39 - Problem Set 5 Problem 3 Problem Two...

Problem Set 5: Problem 3.
Problem: Two identical hockey pucks moving with initial speeds v
A
=
6
5
v and v
B
= v collide as
shown. The coefficient of restitution of the pucks is e . You can ignore the friction of the surface on
which the pucks move.
(a) Determine the velocities of the pucks after impact.
(b) Experimentation shows that Puck A is at rest after the impact when θ = 80 . 13
o
, which corresponds
to cos θ = 6 / 35 . Using your result from Part (a), determine the value of e .
Solution: (a) The line of impact for the hockey pucks is the x axis. So, there is no need to distinguish
between nt and xy coordinates.
Tangential-Velocity Invariance. For pucks A and B, we have the following.
v
Ay
= v
I
Ay
and v
By
= v
I
By
The initial velocities of the pucks are such that v
Ay
= 0 and v
By
= v sin θ . Therefore, the tangential
velocity components after the impact are