Problem:
A block of mass 1.2 kg moving at a speed of 20 cm/s collides head-on with a similar block kept at rest. The coefficient of friction is 3/5. Find the loss of kinetic energy during the collision.

Solution:

Given:
- Mass of the block, m = 1.2 kg
- Initial velocity of the moving block, u = 20 cm/s
- Initial velocity of the stationary block, v = 0 cm/s
- Coefficient of friction, μ = 3/5

Approach:
To find the loss of kinetic energy during the collision, we need to calculate the final velocity of the blocks after the collision and then determine the change in kinetic energy.

1. Find the final velocity of the blocks after the collision.
2. Calculate the change in kinetic energy.

Calculations:

Step 1: Find the final velocity of the blocks after the collision:
- Since the blocks collide head-on, the total momentum before the collision is equal to the total momentum after the collision.
- The initial momentum before the collision is given by:
- Initial momentum of the moving block = mass of the moving block * initial velocity of the moving block
= 1.2 kg * 20 cm/s
- Initial momentum of the stationary block = mass of the stationary block * initial velocity of the stationary block
= 1.2 kg * 0 cm/s (as the block is at rest)
- The total momentum before the collision = initial momentum of the moving block + initial momentum of the stationary block

- Let the final velocity of both blocks after the collision be v.
- The final momentum after the collision is given by:
- Final momentum of the moving block = mass of the moving block * final velocity of the moving block
= 1.2 kg * v
- Final momentum of the stationary block = mass of the stationary block * final velocity of the stationary block
= 1.2 kg * v
- The total momentum after the collision = final momentum of the moving block + final momentum of the stationary block

- According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
- Therefore, we have the equation:
Total momentum before the collision = Total momentum after the collision

- Solving the equation, we get:
(1.2 kg * 20 cm/s) + (1.2 kg * 0 cm/s) = (1.2 kg * v) + (1.2 kg * v)
24 kg·cm/s = 2.4 kg·v
v = 24 kg·cm/s / 2.4 kg = 10 cm/s

- Therefore, the final velocity of both blocks after the collision is 10 cm/s.

Step 2: Calculate the change in kinetic energy:
- The initial kinetic energy before the collision is given by:
- Initial kinetic energy of the moving block = (1/2) * mass of the moving block * (initial velocity of the moving block)^2
= (1/2) * 1.2 kg * (20 cm/s)^2
- Initial kinetic energy of the stationary block