Calculating Energy Loss in a collision

**Hamster Jam** · January 3rd 2010, 07:56 AM

Hi guys, I have a simple question involving the collision of 2 particles of different masses. Particle 1 of mass m is travelling with speed u towards particle 2 of mass 3m which is initially at rest. I have been asked to calculate the energy loss in the impact, however in my notes there is only an example of calculating the energy loss when there is the 'special case' where the masses are the same, which is to use the formula

$\frac{1}{2}mu_{1}^{2} + \frac{1}{2}mu_{2}^{2} - \frac{1}{2}mv_{1}^{2} - \frac{1}{2}mv_{2}^{2}$

How would I construct the above equation given the different masses I have?

Thanks

**CaptainBlack** · January 3rd 2010, 08:59 AM

Originally Posted by Hamster Jam

Hi guys, I have a simple question involving the collision of 2 particles of different masses. Particle 1 of mass m is travelling with speed u towards particle 2 of mass 3m which is initially at rest. I have been asked to calculate the energy loss in the impact, however in my notes there is only an example of calculating the energy loss when there is the 'special case' where the masses are the same, which is to use the formula

$\frac{1}{2}mu_{1}^{2} + \frac{1}{2}mu_{2}^{2} - \frac{1}{2}mv_{1}^{2} - \frac{1}{2}mv_{2}^{2}$

How would I construct the above equation given the different masses I have?

Thanks

The energy lost is equal to the difference in the before and after kinetic energies.

$\Delta KE=\frac{m u}{2} + \frac{(3m) 0}{2} - \frac{m v_1}{2}-\frac{(3m) v_2}{2}$

You have enough information to calculate the before KE but insufficient for the after.

CB

**Hamster Jam** · January 7th 2010, 07:13 AM

The previous question asks me to find the speed acquired by v2 after the collision. I have done this by plugging in my values into the conservation of momentum formula and the law of restitution formula, and solving for v2, so that

$v_{2}=(u(e+1))/4$

So I have v2. Does this mean I can calculate the energy loss?

**DvdHntr** · January 7th 2010, 01:45 PM

Do you have the coefficient (e) or are you assuming elastic and therefore =1?

If that is correct you can use the conservation equations to calculate the kinetic energy loss.

You cannot lose energy per se.

**Hamster Jam** · January 8th 2010, 03:57 AM

It is quite a theoretical natured module, I just have 'e'. I have tried working it out but I'm going round in circles and getting very messy answers, could anyone tell me how to go about calculating energy loss?

**Kiwi_Dave** · January 8th 2010, 01:28 PM

Like CB said the more general equation you are looking for is:

$\Delta KE=\frac 12 m_1u_1^2+\frac 12 m_2u_2^2-\frac 12 m_1v_1^2-\frac 12 m_2v_2^2$

where

$m_1=m$
$m_2=3m$
$u_1=u$
$u_2=0$

Now you just need to calculate $v_1$ and $v_2$ , make the substitutions and out pops the answer.

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