# A ball with a mass of 4 kg moving at 9 m/s hits a still ball with a mass of 18 kg. If the first ball stops moving, how fast is the second ball moving? How much heat energy was lost in the collision?

Jan 28, 2017

required velocity=2m/s and heat energy=126 joules

#### Explanation:

we may note down
${m}_{1} = 4 k g$
${u}_{1} = 9 \frac{m}{s}$
${m}_{2} = 18 k g$
${v}_{1} = 0$
v_2=?
${u}_{2} = 0$
First of all.

we will be applying the principal of conservation of momentum,
i.e,momentum is always conserved.
${m}_{1} \cdot {u}_{1} + {m}_{2} \cdot {u}_{2} = {m}_{1} \cdot {v}_{1} + {m}_{2} \cdot {v}_{2}$

$36 + 0 = 0 + 18 \cdot {v}_{2}$
${v}_{2} = 2 \frac{m}{s}$

With this we have finished 1 part of the question ,now lets proceed to the 2nd part of the question.

to find the heat,i.e lost energy we can subtract initial(before collision) energy and the final (after collision)energies.

$\left({E}_{1}\right) - \left({E}_{2}\right)$=126 joules

We got this by subtracting the kinetic energies. by formulae $\frac{1}{2} m {v}^{2}$

.So in this way we can easily attempt these questions.