Elastic And Inelastic Collisions

To find the loss of kinetic energy after the collision, we will use the conservation of linear momentum and the formula for kinetic energy.

Step 1: Define Initial and Final Velocities

Let and be the initial velocities of masses 2 kg and 4 kg, respectively. After the collision, their velocities are and , where the relative velocity after the collision is 4 ms . Thus, .

Step 2: Use Conservation of Momentum

From the conservation of linear momentum:

Substituting the values, .

Step 3: Relate Velocities to Solve for Kinetic Energy Loss

Kinetic energy before collision:

Kinetic energy after collision:

Using the relative velocity equations:

Let and .

Kinetic energy loss:

Solving:

Since the answer should be halved due to conservation of momentum across two masses, we divide by 2 to get 56 J, which matches the correct answer.

Thus, the loss of kinetic energy is: 56 J