# Kinectic energy of a system of 2 objects

1. Nov 3, 2012

### daivinhtran

is it possible to find kinetic energy of a system of 2 objects when they're both moving at 2 different constant speeds?

because In my textbook, they all assume that one stays at rest and another is moving.

2. Nov 3, 2012

### Vorde

Either method works.

You could either calculate the kinetic energy of each object individually then sum to get the total kinetic energy (it wouldn't matter that the two objects are moving at different speeds because you are calculating them separately). You could also look at the situation from the reference frame of one of the objects, in which case only the other object is moving, and then the kinetic energy of that other object is the total kinetic energy of the system.

Even though total momentum is conserved, kinetic energy by itself is not conserved. This means that different reference frames might show different amounts of kinetic energy in a system.

However all reference frames will agree that kinetic energy is conserved in an elastic collision.

3. Nov 3, 2012

### bp_psy

It depends on what energy you actually want to measure. If you want to measure the kinetic energy of one object with respect to the other, then you can consider one of them stationary and use their relative velocity to find the kinetic energy. If on the other hand you want to find the kinetic energy of the objects with respect to some fixed point ,just add their kinetic energy with respect to that point. In general the two values you obtain are different.

4. Nov 3, 2012

### daivinhtran

But how you calculate the velocity of the center of mass?

THe formula of K of a system is : Ksys = (K of COM) +K(the object relative to the COM)

5. Nov 3, 2012

### bp_psy

$R=\frac{1}{M}\sum_i m_i r_i$

$\frac{dR}{dt}=\frac{d}{dt}\frac{1}{M}\sum_i m_i r_i=\frac{1}{M}\sum_i m_i \frac{dr_i}{dt}=\frac{1}{M}\sum_i p_i$

6. Nov 3, 2012

### daivinhtran

THANKS BUDDYYYYY :d :d