A puck of mass m 1 = 0.25 kg and speed 4.0 m/s collides with a 1.0 kg moving in

Question

A puck of mass m1 = 0.25 kg and speed 4.0 m/s collides with a 1.0 kg moving in the same direction at 1.0 m/s.

a) What is in Kg m/s the overall momentum of the pucks before the collision?

b) What is in Joules the overall kinetic energy of the pucks before the collision?

After the collision, m1 bounces back with a speed of 0.8 m/s.

c)  What is in m/s the speed of the second puck after the collision?

d) What is in Joules the overall kinetic energy of the pucks after the collision?

e) Which of these is statements is the correct statement:
the collision is elastic because momentum is conserved
the collision is elastic because both momentum and kinetic energy are conserved
the collision is elastic because momentum is conserved and m1 bounced back
the collision is elastic because kinetic energy is conserved and m1 bounced back
  the collision is elastic because the masses did not attach
the collision is elastic because the masses did not attach and the momentum is conserved

Explanation / Answer

a) the overall momentum before the collision = m1u1 + m2u2 = 0.25x4 + 1x1 = 1 + 1 = 2 kg m/s

b) the overall kinetic energy before the collision = 0.5m1u12 + 0.5m2u22 = 0.5x0.25x16 + 0.5x1x1 = 2.5 Joules

c) applying conservation of momentum,

m1u1 + m2u2 = m1v1 + m2v2

0.25x4 + 1x1 = 0.25x(-0.8) + 1xv2   (negative sign in v1 because ball bounced back)

v2 = 2 + 0.2 = 2.2 m/s (in the same direction as initial velocity)

d) the total kinetic energy after collision = 0.5m1v12 + 0.5m2v22

  = 0.5x0.25x(-0.8)2 + 0.5x1x1(2.2)2

= 2.5 Joules

e) the collision is elastic because both momentum and kinetic energies are conserved.

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