Question

A ball with a mass of `4 kg` moving at `7 m/s` hits a still ball with a mass of `32 kg`. If the first ball stops moving, how fast is the second ball moving? How much kinetic energy was lost as heat in the collision?

Answer 1

Speed= `0.88ms^-1`, Loss of energy = `75.7J`

Explanation:

You have to solve this question considering the conservation of momentum i.e. total momentum before collision is equal to total momentum after the collision.

Let us consider the ball which is moving initially as A and ball which is in rest as B

Initially,
Momentum of A = `mass*velocity = 4* 7 = 28kgms^-1`
Momentum of B =`mass*velocity= 32* 0 = 0 kgms^-1`
So total momentum before collision = `28 +0 = 28kgms^-1`

Finally,
Let the speed by which B moves be "v"
Momentum of A = `mass*velocity = 4* 0 = 0kgms^-1`
Momentum of B =`mass*velocity= 32* v= 32vkgms^-1`
So total momentum after collision = `0 + 32v = 32v`

Now, total momentum before = total momentum after
So, `28 = 32v`
`v = 28/32`
`v= 0.88 ms^-1` which is the required speed.

Now, For the loss of kinetic energy, calculate kinetic energies both initially and finally and calculate the difference;
Total K.E. before collision = `1/2 mv^2 = 1/2 4 * (7)^2 + 0 = 98J`
Total K.E. after collision = `1/2 mv^2 = 1/2 32 * (0.88)^2 + 0 = 12.3J`

So, Loss in K.E. = 98-12.3 = 75.7J