Question

Consider the following special cases of collisions. In all cases, a cart of m1m1 comes in with a velocity vv and hits a cart m2m2coming in with velocity −v−v (same speed vv from the opposite direction). Most of these are answerable with either intuition or with mathematics. What are the final velocities of both carts if:

a. The collision is elastic, and both carts are the same mass? (Two swords collide in a swordfight)

b. The collision is inelastic, and both carts are the same mass? (Two identical twins charge-tackle each other)

c. The collision is elastic, and the mass of the first cart is much larger than the mass of the second cart? (Sword hits a dagger in a swordfight)

Answer 1

m1 with v

and m2 with - v

The collision is elastic both are the same mass

so their velocity will exchange and now m2 will move with v and m1 will move with - v u can also find this by applying momentum and energy conservation

below the explanation put the velocities with their sign

The collision is inelastic, and both carts are the same mass

apply momentum conservation

m*v + m*-v = 2m*Vf

Vf = 0 so both cart will freez just after they collide

The collision is elastic, and the mass of the first cart is much larger than the mass of the second cart

m1>>>m2 so  

m2/m1 = 0

from the first part formula

v1 = u1 *(1- m2/m1) + 2m2*u2/m1 / ( 1+ m2/m1)

v1 = v

v2 = (-v( m2/m1 -1 ) + 2*v ) / ( ( 1+ m2/m1)

v2 =3v

so velocity of m2 will be 3v in right and  

and velocity of m1 will remains same because it is too big that a small particle collision doesn't change its velocity

i hope this helps if not let me know in comment