Four railroad cars, all with the same mass of 11300 kg, sit on a track, as shown in the figure below. A fifth car of identical mass approaches them with a velocity of 19.3 m/s (to the right). This car collides and couples with the other cars.
(a) What is the kinetic energy of car 5 before the collision?
(b) What is the kinetic energy of all five cars just after the collision?
(c) Is the energy conserved in this collision?
No
Insufficient information
Yes
To solve these questions, we need to understand the concept of kinetic energy and the conservation of energy. Let's go through each part step by step.
(a) What is the kinetic energy of car 5 before the collision?
The formula for kinetic energy is given by:
Kinetic Energy = 1/2 * mass * velocity^2
Given that the mass of car 5 is 11300 kg and its velocity is 19.3 m/s, we can plug in the values into the formula to find the kinetic energy of car 5 before the collision:
Kinetic Energy = 1/2 * 11300 kg * (19.3 m/s)^2
By calculating the expression inside the brackets first, we get:
Kinetic Energy = 11300 kg * 373.49 m^2/s^2
Then we multiply the result by 1/2:
Kinetic Energy = 2123053.5 J
So the kinetic energy of car 5 before the collision is approximately 2,123,053.5 Joules.
(b) What is the kinetic energy of all five cars just after the collision?
Since the fifth car collides and couples with the other four cars, the total mass of the system remains the same as before, which is the sum of the individual masses of the five cars (11300 kg each).
To find the total kinetic energy of all five cars after the collision, we can simply multiply the mass of the system by the final velocity squared and divide by 2, using the same formula as above:
Kinetic Energy = 1/2 * (mass of the system) * (final velocity)^2
The final velocity will be the same for all the cars since they are now coupled together. However, we need more information to calculate this final velocity, so we cannot determine the kinetic energy of all five cars just after the collision without additional data.
(c) Is the energy conserved in this collision?
To determine if the energy is conserved, we compare the total kinetic energy before and after the collision. If they are equal, then the energy is conserved. However, since we don't have enough information about the final velocity of the system, we cannot determine if the energy is conserved in this collision. Therefore, the answer is "insufficient information."