collisions in dimensions?

Question

john (mass 80 kg) is skating when he sees his best friend (mass 20 kg) whith his back turned up ahead. He comes behind his friend grabs him and rolls off at 3.0 m/s. What is johns speed before he grabbed friend (ignore friction)



I dontreally know where to begin... i tried a couple of formulas in the book..... can someone talk me through setting up this problem...... also is this elastic or inelastic? i thought it was inelastic so i was using formulas they gave for that so maybe that s what i got wrong or maybe i wasn't plugging things in right.... please talk me through and explain so i can understand this better for my other collision problems thank you

Answer 1

If I'm reading it correctly, it's inelastic, since John and his friend end up with the same final velocity.

Thus, while momentum is conserved (as it is conserved in all collisions), the total kinetic energy is not. This makes our life much simpler, for with elastic collisions we must solve a system of equations which includes the initial and final kinetic energies.

The sum of the initial momentums should equal the final momentum of their combined mass:
m1*v1 + m2*v2 = (m1 + m2)*vf
Assuming his friend was at rest:
80*v1 + 0 = (100)*3
Thus v1 = 300/80 = 3.75 m/s

This makes sense, that he would be traveling faster before the collision. Since his friend is considerably lighter and not moving, then the collision would take only a little momentum away from him, and since his mass doesn't change this requires a small reduction in velocity.

All this is assuming that I read the question correctly; assuming that his friend was not moving and that this was an inelastic collision.

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Just for your information, I generally relate elastic collisions to billiard balls, and inelastic collisions to automobile accidents where the vehicles stick together. With the billiard balls, the balls compress only a negligible amount, and so their momentum is "perfectly" conserved, as is their kinetic energy. However, with the automobiles, the body crumples. It should make sense that it takes energy to crumple the body. Thus, not all of the initial kinetic energy will remain in the system after the collision, since much of it was lost to the crumpling and heat. We must make the assumption that the collision is "perfectly inelastic" (the vehicles stick together) to make it easily solvable, since it is incredibly difficult, if not impossible, to measure the energy lost in the crumpling of the automobile accident.

Answer 2

Nothing to do with elastic if they both roll off together (he grabbed him, right). So, after the grab, their combined mass is 100 Kg and their speed is 3.0 M/s, so you know their combined kinetic energy. That must have been John's energy before the grab, so we can just use his mass alone (80 Kg) and figure out what speed he was traveling to have the required energy. It is a conservation of energy problem.....the pair had the same combined energy both before and after the grab.