A 3 kg toy car with a speed of 10 m/s collides head-on with a 2 kg car traveling in the opposite direction with a speed of 2 m/s. If the cars are locked together after the collision with a speed of 5.20 m/s, how much kinetic energy is lost?
see other post.
To calculate the kinetic energy lost in the collision, we first need to find the initial total kinetic energy before the collision and the final total kinetic energy after the collision. Then, we can subtract the final kinetic energy from the initial kinetic energy to determine the amount of kinetic energy lost.
1. Calculate the initial total kinetic energy:
- The kinetic energy of an object is given by the formula: KE = (1/2) * mass * (velocity)^2.
- For the first car, the mass is given as 3 kg and the speed is 10 m/s, so the initial kinetic energy of the first car is KE1 = (1/2) * 3 kg * (10 m/s)^2.
- For the second car, the mass is given as 2 kg and the speed is 2 m/s, so the initial kinetic energy of the second car is KE2 = (1/2) * 2 kg * (2 m/s)^2.
- The initial total kinetic energy is the sum of the kinetic energy of both cars: Initial total KE = KE1 + KE2.
2. Calculate the final total kinetic energy:
- After the collision, the two cars are locked together and move with a speed of 5.20 m/s.
- The mass of the combined system is the sum of the masses of the two cars: Combined mass = 3 kg + 2 kg.
- The final kinetic energy is given by: Final KE = (1/2) * Combined mass * (final velocity)^2.
3. Calculate the kinetic energy lost:
- The kinetic energy lost is the difference between the initial and final kinetic energies: KE lost = Initial total KE - Final KE.
Now you can substitute the given values into the calculations to find the answer.