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?
1. No
2. Insufficient information
3. Yes
a. KE = 0.5m*V^2
KE = 0.5*11300*19.3^2 = 2,104,569 J.
b. Momentum = 5 * m*V = m1*V1
5 * 11,300*V = 11,300*19.3
56,500V = 218,090
V = 3.86 m/s.
KE = 0.5*5m*V^2
KE = 0.5*5*11,300*3.86^2 = 420,914 J.
To find the answers to these questions, we need to consider the principle of conservation of energy. According to this principle, the total energy before the collision should be equal to the total energy after the collision.
(a) To find the kinetic energy of car 5 before the collision, we can use the formula for kinetic energy: KE = 1/2 * mass * velocity^2.
Given that car 5 has a mass of 11300 kg and a velocity of 19.3 m/s, we can substitute these values into the formula to find the kinetic energy.
KE = 1/2 * 11300 kg * (19.3 m/s)^2 = 2.16 x 10^6 Joules.
(b) To find the kinetic energy of all five cars just after the collision, we need to find the final velocity of the coupled cars. Since the cars couple together, their total mass will be the sum of their individual masses (4 cars with a mass of 11300 kg each and car 5 with the same mass). Therefore, the total mass will be 5 * 11300 kg = 56500 kg.
The total kinetic energy can then be calculated using KE = 1/2 * mass * velocity^2, where mass is the total mass of the coupled cars and velocity is the final velocity after the collision.
Since we are not given the final velocity, we cannot directly calculate the kinetic energy of all five cars just after the collision. Hence, the answer is "Insufficient information."
(c) To determine if energy is conserved in this collision, we need to compare the total energy before the collision (kinetic energy of car 5) with the total energy after the collision (kinetic energy of all five cars).
If the total energy before the collision is equal to the total energy after the collision, then the energy is conserved. Otherwise, it is not conserved.
Since we don't have enough information to calculate the total energy after the collision, we cannot determine if energy is conserved or not. Hence, the answer is "Insufficient information" as well.