Expression of elastic potential energy

Expression of elastic potential energy

EP=(1/2)kx^2
F=(1/2)kx
K = telescopic force of the catapult

On the difference between completely inelastic collision, completely elastic collision and incompletely elastic collision

Completely inelastic is the combination of the two
Complete elasticity means that the energy is not absorbed by the object at all, but is completely used to change the motion mode of the object. After collision, the speed remains unchanged and the direction changes
Incomplete is that part of the energy makes the object deform, part of the energy changes the way the object moves, and the speed becomes smaller after the collision

Completely elastic collision
How does this formula come from, V1 = [(m1-m2) V10 + 2m2v20] / (M1 + m2)
v2 = [(m2-m1)v20 + 2m1v10] / (m1+m2)
I've been calculating for a long time, but I haven't worked it out,

In complete elastic collision, momentum and kinetic energy are conserved
Momentum conservation: M1 * V10 + M2 * V20 = M1 * V1 + M2 * V2
Kinetic energy conservation: 1 / 2M1 * V10 & # 178; + 1 / 2M2 * V20 & # 178; = 1 / 2M1 * V1 & # 178; + 1 / 2M2 * V2 & # 178;
By solving the binary equations, we can get the following results
v1=(m1*v10-m2*v10+2m2*v20)/(m1+m2)
v2=(2m1*v10-m1*v20+m2*v20)/(m1+m2)
V1 = V10, V2 = V20 omitted