To calculate the kinetic energy lost in the collision, we need to determine the initial and final kinetic energies of the system.
The initial kinetic energy of the system is the sum of the kinetic energies of the two objects before the collision. The kinetic energy (KE) of an object is given by the equation KE = (1/2)mv^2, where m is the mass of the object and v is its velocity.
For the first object with a mass of 4 kg and velocity of 6 m/s, the initial kinetic energy is: KE1 = (1/2) * 4 kg * (6 m/s)^2 = 72 J
For the second object with a mass of 6 kg and velocity of 5 m/s, the initial kinetic energy is: KE2 = (1/2) * 6 kg * (5 m/s)^2 = 75 J
The final kinetic energy of the system is the kinetic energy of the combined mass after the collision.
Since the two objects stick together after the collision, they become one object with a total mass of 4 kg + 6 kg = 10 kg.
The final velocity of the combined object can be found using the principle of conservation of momentum, which states that the total momentum before the collision is equal to the total momentum after the collision. Since the two objects are moving in the same direction, the momentum equation is:
(mass1 * velocity1) + (mass2 * velocity2) = (mass1 + mass2) * velocity_final
(4 kg * 6 m/s) + (6 kg * 5 m/s) = 10 kg * velocity_final
24 kg·m/s + 30 kg·m/s = 10 kg * velocity_final
54 kg·m/s = 10 kg * velocity_final
velocity_final = 54 kg·m/s / 10 kg velocity_final = 5.4 m/s
The final kinetic energy (KE_final) of the system is given by: KE_final = (1/2) * total_mass * velocity_final^2
KE_final = (1/2) * 10 kg * (5.4 m/s)^2 KE_final = 145.8 J
The kinetic energy lost in the collision is the difference between the initial kinetic energy and the final kinetic energy:
Kinetic energy lost = Initial kinetic energy - Final kinetic energy Kinetic energy lost = (KE1 + KE2) - KE_final Kinetic energy lost = (72 J + 75 J) - 145.8 J Kinetic energy lost = 147 J - 145.8 J Kinetic energy lost ≈ 1.2 J
Therefore, approximately 1.2 Joules of kinetic energy was lost in the collision.