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

Does the data support the claim? Explain.

A. 

Yes, because the total momentum of the system was conserved when there was no net force on the system.

B. 

Yes, because the total momentum of the system was conserved when there was a net force on the system.

C. 

No, because the total momentum of the system was not conserved when there was a net force on the system.

D. 

No, because the total momentum of the system was not conserved when there was no net force on the system.

Answer 1

Compute total momentum before and after the push.

Before:
- Skater 1: p1 = 55.0 kg × 4.00 m/s = 220.0 kg·m/s
- Skater 2: p2 = 50.0 kg × 3.49 m/s = 174.5 kg·m/s
- Total before = 220.0 + 174.5 = 394.5 kg·m/s

After:
- Skater 1: p1' = 55.0 kg × 2.50 m/s = 137.5 kg·m/s
- Skater 2: p2' = 50.0 kg × 5.14 m/s = 257.0 kg·m/s
- Total after = 137.5 + 257.0 = 394.5 kg·m/s

Since total momentum before equals total momentum after, the data support the claim that total momentum is conserved when there is no net external force on the system. Answer: A.