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?
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To find the amount of kinetic energy lost during the collision, we need to calculate the initial kinetic energy and the final kinetic energy of the system.
1. Calculate the initial kinetic energy (KE_initial):
- For the first car with a mass of 3 kg and a speed of 10 m/s, the initial kinetic energy is given by KE1 = (1/2) * m1 * v1^2.
- Substituting the values, KE1 = (1/2) * 3 kg * (10 m/s)^2 = 150 J.
- For the second car with a mass of 2 kg and a speed of 2 m/s, the initial kinetic energy is given by KE2 = (1/2) * m2 * v2^2.
- Substituting the values, KE2 = (1/2) * 2 kg * (2 m/s)^2 = 4 J.
- The total initial kinetic energy is given by KE_initial = KE1 + KE2 = 150 J + 4 J = 154 J.
2. Calculate the final kinetic energy (KE_final):
- For the cars locked together with a mass of (3 kg + 2 kg) = 5 kg and a speed of 5.20 m/s, the final kinetic energy is given by KE_final = (1/2) * m_total * v_final^2.
- Substituting the values, KE_final = (1/2) * 5 kg * (5.20 m/s)^2 = 67.6 J.
3. Calculate the kinetic energy lost:
- The kinetic energy lost is given by KE_lost = KE_initial - KE_final.
- Substituting the values, KE_lost = 154 J - 67.6 J = 86.4 J.
Therefore, the amount of kinetic energy lost during the collision is 86.4 J.