Question

A metal ball of mass 2 kg moving with a speed of 10m/s collides with 3 kg at rest. After collision both ball move together then the loss in kinetic energy is ??
plzzz solve it stepwise with a reason

Answer 1

Hi.
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Answer 2

Given:

The mass of the ball = 2kg

The speed of the ball is 10m/s collides with 3 kg at rest.

To Find:

The loss of the kinetic energy

Solution:

Let the speed of the metal ball be v1 = 10m/s

The mass of the stationary ball is given as 2 kg

Now, to find the loss of kinetic energy,

Applying the law of conservation of momentum,

$m_{1} v_{1} + m_{2} v_{2} = (m_{1} m_{2})^{v}$

The same can also be written as

v = $\frac{m_{1} v_{1} + m_{2} v_{2} }{m_{1} + m_{2} }$

Now, substituting the values in the equation,

 = $\frac{(2*10)+(3*10)}{2+3}$

It is given the question that $m_{1}$ = 2kg $m_{2}$ = 3kg, $v_{1}$ = 10m/s

= 10×2/5

= 4m/s

Now, we find the initial kinetic energy, using the formula 1/2 + (m1+m2)²

  = 1/2 × 2 ×(10)²

  = 100J

∴ The initial kinetic energy is 100J

Then we find the final kinetic energy, using the same formula used to find the initial energy.

= 1/2 × (3+2) ×(4)²

= 1/2 × 6 × 16

= 40J

∴ The final kinetic energy is 40J

Now, the loss in kinetic energy = initial kinetic energy - final kinetic energy

 = 100J - 40J

 = 60J

Therefore, after Collison both ball moves together then the loss in kinetic energy is 60J.