Final answer:
To find how far each skater travels, we use the principle of conservation of momentum and the idea that the center of mass of the system remains stationary. By setting up equations for the momentum of each skater and solving them with respect to the center of mass, we can determine the distance each skater travels.
Step-by-step explanation:
The student's question involves the conservation of momentum and how two skaters pulling on a rope with equal force but different masses will move towards each other. According to momentum conservation, the center of mass of the system of two skaters will not move if there are no external forces acting on the system, such as friction in this case.
Both skaters will meet at the center of mass of the system. The skater with the larger mass will travel a shorter distance, while the skater with the smaller mass will travel a longer distance, with their combined distances adding up to the original separation between them of 8.2 meters.
- Let the distances travelled by the 58 kg and 50 kg skaters be d58 and d50, respectively.
- Since they exert equal force over the same time, their momenta will be equal and opposite, so m58 × v58 = m50 × v50.
- Because the total momentum is zero (initially they were at rest and no external forces act), we have d58 + d50 = 8.2 m.
- The center of mass R can be found using R = (m58 × d58 + m50 × d50)/(m58 + m50). Since R = 0 by symmetry, we get d58 × 58 = d50 × 50.
- Solving these two equations will give the distances travelled by each skater, which are inversely proportional to their masses.