Question

1. why must the total momentum before and after the push be the same? 6. imagine skater b was twice as heavy (80 kg). how would the results change? 7. think of a real - world situation (outside of skating) where momentum conservation plays an important role. explain. 8. why does the frictionless surface matter in this experiment?

Explanation:

1. According to the law of conservation of momentum, in an isolated system (no external forces), total momentum is conserved. So, the total momentum before and after the push is the same.
2. If Skater B is heavier (80 kg), with conservation of momentum, Skater A would have a greater velocity after the push compared to when Skater B had a lower mass, as momentum \(p = mv\) and the total initial momentum is 0.
3. In a car - crash, momentum conservation is crucial. When two cars collide, the total momentum before the collision equals the total momentum after the collision. This helps in analyzing the speeds and directions of cars before and after the crash.
4. A frictionless surface matters because friction is an external force. In a friction - less environment, the system is closer to being isolated, allowing momentum conservation to be clearly demonstrated without the complication of frictional forces changing the motion of the skaters.

Answer:

1. Due to the law of conservation of momentum in an isolated system.
2. Skater A would have a greater velocity after the push.
3. In car - crashes, total momentum before and after the collision is conserved, helping in analysis.
4. To make the system closer to an isolated one and avoid the effect of external frictional forces.