A 5 kg toy car with a speed of 6 m/s collides head-on with a stationary 1 kg car. After the collision, the cars are locked together with a speed of 5.00 m/s. How much kinetic energy is lost in the collision?

conservation of momentum

5*6+0=6*5

final energy=1/2 m v^2=3*25
initial KE=1/2 m v^2=2.5*36
amountlost is difference

To determine the amount of kinetic energy lost in the collision between the two cars, we need to calculate the initial and final kinetic energies of the system.

1. Calculate the initial kinetic energy (KE_initial) of the system before the collision using the formula:

KE_initial = 1/2 * m1 * v1^2 + 1/2 * m2 * v2^2

Here, m1 is the mass of the first car (5 kg) and v1 is its initial velocity (6 m/s). Similarly, m2 is the mass of the second car (1 kg) and v2 is its initial velocity (0 m/s) since it is stationary.

Plugging in the values:

KE_initial = 1/2 * 5 kg * (6 m/s)^2 + 1/2 * 1 kg * (0 m/s)^2

KE_initial = 90 J + 0 J

KE_initial = 90 J

2. Calculate the final kinetic energy (KE_final) of the system after the collision using the formula:

KE_final = 1/2 * (m1 + m2) * v_final^2

Here, m1 + m2 is the combined mass of both cars (5 kg + 1 kg = 6 kg). The final velocity (v_final) of the cars after collision is 5 m/s.

Plugging in the values:

KE_final = 1/2 * 6 kg * (5 m/s)^2

KE_final = 1/2 * 6 kg * 25 m^2/s^2

KE_final = 75 J

3. Calculate the kinetic energy lost (KE_lost) in the collision by subtracting the final kinetic energy from the initial kinetic energy:

KE_lost = KE_initial - KE_final

KE_lost = 90 J - 75 J

KE_lost = 15 J

Therefore, the amount of kinetic energy lost in the collision between the two cars is 15 Joules.