first, find the velocity of the two cars after the collision since they stick together. The law of conservation of momentum states that the total momentum before the collision equals the total momentum after the collision.
1. Calculate the initial momentum (before the collision) of both cars:
Momentum (P_initial) = mass (m) * velocity (v)
For Car 1 (900 kg):
P1_initial = (900 kg) * (10 m/s) = 9000 kg·m/s
For Car 2 (1100 kg) at rest:
P2_initial = (1100 kg) * (0 m/s) = 0 kg·m/s
total initial momentum = P1_initial + P2_initial = 9000 kg·m/s
2. Calculate the total mass (m_total) of the two cars after the collision since they stick together:
m_total = mass of Car 1 + mass of Car 2
m_total = 900 kg + 1100 kg = 2000 kg
3. Use the conservation of momentum to find the velocity (v_final) of the cars after the collision:
P_initial = P_final
9000 kg·m/s = (2000 kg) * (v_final)
Now, solve for v_final:
v_final = 9000 kg·m/s / 2000 kg = 4.5 m/s
Now that we have found the velocity after the collision (v_final), we can calculate the kinetic energy before and after the collision.
4. Calculate the initial kinetic energy (before the collision):
Kinetic Energy (KE_initial) = (1/2) * mass * velocity^2
For Car 1:
KE1_initial = (1/2) * 900 kg * (10 m/s)^2 = 45000 J (joules)
For Car 2 (at rest):
KE2_initial = (1/2) * 1100 kg * (0 m/s)^2 = 0 J (joules)
The total initial kinetic energy = KE1_initial + KE2_initial = 45000 J
5. Calculate the final kinetic energy (after the collision):
KE_final = (1/2) * m_total * v_final^2
KE_final = (1/2) * 2000 kg * (4.5 m/s)^2 = 20250 J (joules)
Now, we can answer the questions:
- The kinetic energy before the collision is 45000 J.
- The kinetic energy after the collision is 20250 J.
- The change in kinetic energy is the difference between the initial and final kinetic energies:
Change in KE = KE_initial - KE_final = 45000 J - 20250 J = 24750 J
the change in kinetic energy during the collision is 24750 joules.