Which is more damaging?
Case1.: A man on roller skates moving at 30 km/hr rams into a stationary car
Case2.: A car moving at 30 km/hr with its engine switched off rams into a stationary man on roller skates.
Which case would cause more damage to the man. Case1 or case2. I do not know the answer for sure. The relative velocity is the same in both cases but not the kinetic energy. Please type your answer in comments. Thanks in advance.
Case 2 will cause more damage because the momentum transfer in case 2 is much higher than Case1. Momentum transfer depends upon the mass of the body in motion (if speed is equal ). This is the reason when trains collide they crush train coaches like cardboard boxes no matter how slow they are while colliding.
Mir,
The collisions are identical. The only that that differs is that the observer is either moving with the car or with the person.
Physics (Newtonian and Relativistic) cannot change by simply moving to another inertial frame.
Arockianathan Samson Abhishek Verma
Chaps,
Can you explain why you chose the answers that you did?
I submit to you that the two events (moving car strikes static person, and static car hit by moving person) are different *only* because of the motion of us, the observer, watching the event.
How, in that case, can our motion, influence the amount of momentum and energy that is exchanged?
I care less about the right answer than I do about your thinking process - it's instructive to know how non-intuitive physics is, and so present it more clearly for students.
If the stationary car is heavy enough it will presumably remain stationary when hit by the man, whereas the stationary man on roller skates will presumably be moved along by the moving car.
Karl Pfeifer Exactly.
And the effect on the person (and the car) is the same. I assume that the roller skate reference is simply to ensure that the person 'sticks' to the car and we can discard the friction of them being dragged along the underside of the car.
(!)
In the frame of the moving car:
momentum of car = 0
momentum of person = mass_of_person x closing speed
Total momentum before = m_person . v_closing + 0
After the collision, in which the person semi-elastically sticks to the car, draped over the bonnet;
total momentum = (m_car+m_person) x v_after
If the person is much lighter than the car, then in this frame the composite object of car and person moves little after the impact. The person is brought to rest, and the car barely rolls.
Total momentum change of person = m_person x closing speed
Let's look at it in the same frame as the moving person. Now, the person is at rest, and is struck by a car moving at 'closing speed'.
The person is carried away by the car, and experiences exactly the same momentum change. The car is barely slowed by the impact, and the composite body of car+person travels at almost the original 'closing_speed'.
The question could do with a little more detail to ensure that we have inelastic collisions - but if the bodies stick (poor choice of words, sorry) then the person experiences the same damage.
Aswant Kumar Sharma
It's a gedanken experiment, but is readily done.
1) Drive to a given speed, and pop the gearbox into neutral.
2) Coast down hill and reach a level bit of road (and an unwitting roller-skater)
3) etc.
James Garry
My intuitive reasoning is much simpler. Based on my grade 8 or 9 science, whether the man goes from 30 to 0 or 0 to 30, the inertia overcome is the same; in the latter case because the man moves with the train it can do no more damage. In effect he's now just a part of the train.
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