Question

Two motor vehicles A and B are moving along a horizontal straight road in opposite directions. Vehicle A of mass 3 500 kg is moving with a speed of 14 m/s and vehicle B, mass 2 000 kg is moving with a speed 20 m/s. They collide and move together. [4] Calculate the change in kinetic energy.

Answer 1

To calculate the change in kinetic energy, we need to find the initial kinetic energy and the final kinetic energy.

The initial kinetic energy of vehicle A is given by the equation:

K.E. = 0.5 * mass * speed^2

Substituting the values:

K.E. = 0.5 * 3500 kg * (14 m/s)^2 = 686,000 J

The initial kinetic energy of vehicle B is given by the equation:

K.E. = 0.5 * mass * speed^2

Substituting the values:

K.E. = 0.5 * 2000 kg * (20 m/s)^2 = 400,000 J

After the collision, the vehicles move together with a final velocity. To find the final velocity, we use the conservation of momentum:

(mass A * velocity A) + (mass B * velocity B) = (mass A + mass B) * final velocity

(3500 kg * 14 m/s) + (2000 kg * (-20 m/s)) = (3500 kg + 2000 kg) * final velocity

49,000 kg*m/s + (-40,000 kg*m/s) = 5500 kg * final velocity

9000 kg*m/s = 5500 kg * final velocity

final velocity = 9000 kg*m/s / 5500 kg = 1.636 m/s

The final kinetic energy is given by:

K.E. = 0.5 * (mass A + mass B) * final velocity^2

Substituting the values:

K.E. = 0.5 * (3500 kg + 2000 kg) * (1.636 m/s)^2 = 11,242.5 J

The change in kinetic energy is given by:

Change in K.E. = final kinetic energy - initial kinetic energy

Change in K.E. = 11,242.5 J - 686,000 J = -674,757.5 J.

Therefore, the change in kinetic energy is -674,757.5 J.