Question

A 2.0 kg puck is moving east at 5.5 m/s. It catches up to and collides with a second identical puck moving due east at 3.0 m/s. The collision is perfectly inelastic.
What is the resulting velocity of the pucks?
What is the initial kinetic energy Eki of the system?
What is the change in kinetic energy, ΔEk, of the system as a result of the collision?
If the mass m is doubled, but the initial velocities are unchanged, does the resulting velocity increase, decrease, or remain unchanged?

Answer 1

2.0*5.5 + 2.0*3.0 = 4.0v
v = 4.25 m/s east

KEi = 1/2 * 2.0 * 5.5^2 + 1/2 * 2.0 * 3.0^2 = 39.25 J
KEf = 1/2 * 4.0 * 4.25^2 = 36.125 J

doubling the mass does not affect the velocity. Note that
2m1*v1 + 2m2*v2 = (2m1+2m2)v
2(m1*v1 + m2*v2) = 2(m1+m2)v
the 2 just cancels out

since KE = 1/2 mv^2, doubling the mass doubles the KE