# Conservation of kinetic energy

1. Nov 11, 2012

### kreb11

1. The problem statement, all variables and given/known data
I am asked to explain the conservation of kinetic energy

I am having trouble finding this..I do know that kinetic eneergy is conserved in an elastic collision and part of the KE is changed to some other form of energy in an inelastic collision

2. Nov 11, 2012

### Abhinav R

A perfectly elastic collision is defined as one in which there is no loss of kinetic energy in the collision. An inelastic collision is one in which part of the kinetic energy is changed to some other form of energy in the collision. Any macroscopic collision between objects will convert some of the kinetic energy into internal energy and other forms of energy, so no large scale impacts are perfectly elastic. Momentum is conserved in inelastic collisions, but one cannot track the kinetic energy through the collision since some of it is converted to other forms of energy. Collisions in ideal gases approach perfectly elastic collisions, as do scattering interactions of sub-atomic particles which are deflected by the electromagnetic force. Some large-scale interactions like the slingshot type gravitational interactions between satellites and planets are perfectly elastic.

Collisions between hard spheres may be nearly elastic, so it is useful to calculate the limiting case of an elastic collision. The assumption of conservation of momentum as well as the conservation of kinetic energy makes possible the calculation of the final velocities in two-body collisions.

We are now going to see an example of how to use this “principle” which i am going to call the “principle of conservation of kinetic energy”.

Fig 1 below shows two objects travelling towards each other and fig 2 shows the two objects separating after the two objects have separated.

So if the principle of conservation of kinetic energy applies then it means that Sum of kinetic energy before collision = sum of kinetic energy after collision

http://lh3.ggpht.com/_MLcxcpYx4ws/S4iqI2bfwVI/AAAAAAAAAbI/zY5-598E6dQ/s1600-h/clip_image001%5B5%5D.gif

Fig 1 Before collision

Before the collision

Sum of kinetic energy before collision = kinetic energy of object 1 + kinetic energy of object 2

= 1/2m1u12 + 1/2m2v12

http://lh3.ggpht.com/_MLcxcpYx4ws/S4iydzx3GVI/AAAAAAAAAbQ/YgNllKXs98c/s1600-h/clip_image001%5B6%5D%5B4%5D.gif

Fig 2 After collision

After the collision
Sum of kinetic energy after collision = kinetic energy of object 1 + kinetic energy of object 2

= 1/2m1u22 + 1/2m2v22

If you refer back to the principle then

Sum of kinetic energy before collision = sum of kinetic energy after collision

1/2m1u12 + 1/2m2v12 = 1/2m1u22 + 1/2m2v22

Last edited: Nov 11, 2012