Question

Roller Skating Momentum

Two roller skaters are skating on a straight roller skating track and practicing the skills they need to play roller derby. Roller Skater 1 is behind Roller Skater 2. Roller Skater 1 pushes Roller Skater 2 from behind to help Roller Skater 2 gain velocity, as shown in the picture. 



A student took data on the roller skaters in an attempt to support the claim, "the total momentum of a system of objects is conserved when there is no net force on the system." The table shows the data.

Roller SkaterMass (kg)Velocity Before Push (m/s)Velocity After Push (m/s)155.04.002.50250.03.495.14

Multiple Choice Question

Which statement MUST be true in order for the data to support the claim?

A. 

The momentum of Roller Skater 1 before the push is more than her momentum after the push.

B. 

The momentum of Roller Skater 2 before the push is less than her momentum after the push.

C. 

The combined momentum of the roller skaters before the push must be the same as the combined momentum of the roller skaters after the push.

D. 

The combined momentum of the roller skaters before the push must be greater than the combined momentum of the roller skaters after the push.

Answer 1

Answer: C.

Reason: Conservation of momentum refers to the total momentum of the system. For the data to support the claim, the combined momentum before the push must equal the combined momentum after the push.

Check with the numbers:
- Skater 1: p_before = 55.0·4.00 = 220.0 kg·m/s; p_after = 55.0·2.50 = 137.5 kg·m/s.
- Skater 2: p_before = 50.0·3.49 ≈ 174.5 kg·m/s; p_after = 50.0·5.14 = 257.0 kg·m/s.

Total before = 220.0 + 174.5 = 394.5 kg·m/s; total after = 137.5 + 257.0 = 394.5 kg·m/s. They are equal, so C is correct.