Question

Two ice skaters are gliding together along the ice, both moving at a constant velocity vi = 4.39 m/s (sliding without exerting a force). The first skater, the one in the back, with mass M1 = 79.6 kg, pushes the second skater, the one in front, with mass M2 = 57.3 kg, directly forward in the direction they are initially moving.

After the push the first skater is not moving (velocity = 0) and the second skater is moving with a final velocity of vf.

How much energy must the first skater provide to make this happen? Give your answer in Joules to at least three significant digits to avoid being counted off for rounding. Do not include units with your answer.

(Note: You can assume the friction of the ice on the skaters can be neglected and the front skater does not expend any energy.)

Answer 1

Initial momentum of the skaters, Pi = M1vi + M2Vi = (M1 + M2) vi
= (79.6 + 57.3) x 4.39
= 600.991 kg m/s

Final momentum, Pf = M2 vf
= 57.3 vf

Using conservation of momentum, Pi = Pf
600.991 = 57.3 vf
vf = 10.49 m/s

Initial energy of the system, Ei = 1/2 (M1 + M2) vi²
= 0.5 x (79.6 + 57.3) x 4.39²
= 631.75 J

Final energy of the system, Ef = 1/2 M2vf²
= 0.5 x 57.3 x 10.49²
= 3151.75 J

So, the first skater must provide an energy of E = Ef - Ei
= 3151.75 - 631.75
= 2520 J