Question

Please answer with a written response rather than calculations:

-describe conservation of momentum in elastic AND inelastic collisions

-describe the path of the center of mass for two colliding objects

-explain the relationship between conservation of energy in a collision and coefficient of restitution

-explain conversions between kinetic, gravitational potential, and magnetic potential energy

thanks

Answer 1

Let us consider a collision in one dimensions, it means both particles are travel along straight line, after collision they again travel along straight line.

1. According to law of conservative of linear momentum, the total linear momentum of particles before collision is equal to the total linear momentum of particles after collision.

Law of conversation of linear momentum is valid in both elastic as well as inelastic collision.

2. Weather the collision is elastic or inelastic, center of mass of colliding particles is always travel along the same path before and after collision. Suppose we have two two particles moving along straight line, then they collide for a short period of time. The center of mass of two particles lie inbetween the line joining the two particles before and after the collision. No matter whether particles are going along straight line or going into plane after collision, the center of mass of two particles is travel along same path.

3. According to the law of conservative of total energy, total energy of a system is conserved, it can be transferred from one form to another. In case of elastic collision, there is no loss of kinetic energy during collision. Total energy is conserved in case of elastic collision. There is loss of kinetic energy in case of inelastic collision which can be transferred from kinetic to sound or heat energy. But total energy is remain conserved.

Coefficient of restitution is measure of elasticity of collision. It is equal to the ratio of relative velocity of separation after collision to the relative velocity of approach before collision. It is denoted by symbol e.

For perfectly inelastic collision it value is 0 and for elastic collision it's value is 1. In general for practical collision it lies between 0 and 1 I:e 0<e<1.

4. Conservation of kinetic energy is valid only in elastic collision. It means total kinetic energy of incoming particles is equal to the total kinetic energy of outgoing particles.

Gravitational potential energy is conserved. It can be maximum when object is at maximum hieght as object falls down, gravitational potential energy starts converting into kinetic energy. And at the bottom whole potential energy is changed into kinetic energy.

Magnetic potential energy is also conserved.it is basically equal to the scaler product of magnetic moment and magnetic field. Magnetic potential energy is maximum when both are lies in same line. It is zero when both are lies in opposite direction. And it is zero when magnetic moment is perpendicular to the magnetic field.