Q5.7 A simple collision (S)
On an ice rink, a man and a woman collide. Before the collision, the man (mass 80 kg) was travelling at 20 kmh-1, while the woman (mass 50 kg) was travelling in the same direction at 5 kmh-1. When they collide, the woman grabs the man and they slide along together.- Is it reasonable to use the principle of conservation of momentum in this problem?
- Can one expect that mechanical energy will be conserved here?
- What is the speed of the two skaters just after the collision?
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Solution
- If air resistance and friction with the ice are small enough to be neglected, it is reasonable to use the principle of conservation of momentum. If not, then the man - woman system cannot really be considered in isolation, and the total momentum will not be conserved. However, we would expect that these frictional losses would be small, and use conservation of momentum.
- It is not reasonable to expect that mechanical energy be conserved, even if we neglect frictional losses to the surroundings, as some of the mechanical energy might be transferred into heat during the collision process.
We can calculate the speed after the collision by equating each component of the momentum before and after the collision. (But there is only one component of the momentum, because everyone moves in a straight line). Denoting pre-collision velocities with a '
mmanv'man+mwomanv'woman=(mman+mwoman)vSolving for v we obtain v=(80×20+50×5)/(80+50)=14.2 kmh-1