Two manned satellites approaching one another at a relative speed of 0.500 m/s intend to dock. The first has a mass of 3.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. Assume that the positive direction is directed from the second satellite towards the first satellite.(b) What is the loss of kinetic energy in this inelastic collision?
To find the loss of kinetic energy in this inelastic collision, we need to calculate the initial kinetic energy and the final kinetic energy of the system.
1. Calculate the initial kinetic energy:
The formula for kinetic energy is KE = 1/2 * mass * velocity^2.
For the first satellite with a mass of 3.50 × 10^3 kg, the initial kinetic energy is:
KE1 = 1/2 * 3.50 × 10^3 kg * (0.500 m/s)^2.
For the second satellite with a mass of 7.50 × 10^3 kg, the initial kinetic energy is:
KE2 = 1/2 * 7.50 × 10^3 kg * (0.500 m/s)^2.
2. Calculate the final kinetic energy:
In an inelastic collision, the two objects stick together and move as a single unit after the collision. Therefore, the final velocity of the system will be the same as the initial velocity of the first satellite.
Since the final velocity is the same as the initial velocity of the first satellite, the final kinetic energy can be found using the formula:
KE_Final = 1/2 * (mass1 + mass2) * velocity^2.
KE_Final = 1/2 * (3.50 × 10^3 kg + 7.50 × 10^3 kg) * (0.500 m/s)^2.
3. Calculate the loss of kinetic energy:
The loss of kinetic energy can be calculated by subtracting the final kinetic energy from the initial kinetic energy.
Loss of kinetic energy = KE_Initial - KE_Final.
Now, you can plug in the values and calculate the loss of kinetic energy.