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= 1/2mv*v
1/2(11300)(19.3)2= 2104568.5 J
b.) Mtotal=5carts*11300kg=56500kg
Vfinal= Pfinal/Mtotal
(11300)(19.3)/56500= 3.86
KEfinal= 1/2(Mtotal)(Vfinal)
1/2(56500)(3.86)2= 420913.7
c.) carts stick together so perfectly inelastic which means energy is NOT conserved
(a) Well, before the collision, car 5 would be feeling pretty kinetic, wouldn't it? Its kinetic energy can be calculated using the formula KE = 0.5 * mass * velocity^2. So plug in the values and let's do some math! KE = 0.5 * 11300 kg * (19.3 m/s)^2.
(b) After the collision, all five cars are going to have a blast...of kinetic energy! So let's find out how much energy they have. Just add up the kinetic energies of each car. Each car has the same mass and the same velocity, so all we need to do is multiply the individual KE we found in part (a) by 5. That's 5 times the fun, I mean, 5 times the KE.
(c) The big question: is the energy conserved in this collision? Well, let me think for a second... Hmm... The information given doesn't really hint at any external forces acting on the system, so I'm going to go ahead and say yes, the energy is conserved in this collision. Energy conservation is no joking matter, after all!
So to recap:
(a) The kinetic energy of car 5 before the collision is 0.5 * 11300 kg * (19.3 m/s)^2.
(b) The kinetic energy of all five cars just after the collision is 5 times the answer from part (a).
(c) The energy is conserved in this collision, my friend!
To answer these questions, we will need to use the conservation of momentum and the conservation of kinetic energy principles.
(a) To find the kinetic energy of car 5 before the collision, we can use the formula:
Kinetic energy = (1/2) * mass * velocity^2
Given that the mass of car 5 is identical to the other cars and its velocity is 19.3 m/s, we can calculate its kinetic energy:
Kinetic energy of car 5 before the collision = (1/2) * 11300 kg * (19.3 m/s)^2
(b) To find the combined kinetic energy of all five cars just after the collision, we need to find the final velocity of the system. Assuming an elastic collision (where kinetic energy is conserved), the momentum before the collision is equal to the momentum after the collision:
Momentum before collision = Momentum after collision
The momentum of each car is given by the product of its mass and velocity:
Momentum before collision = mass_car1 * velocity_car1 + mass_car2 * velocity_car2 + mass_car3 * velocity_car3 + mass_car4 * velocity_car4 + mass_car5 * velocity_car5
After the collision, the cars are coupled, so they move together as one unit. Since their masses are the same, their velocities will be the same:
Momentum after collision = (mass_car1 + mass_car2 + mass_car3 + mass_car4 + mass_car5) * final_velocity
Since both momenta are equal, we can set them equal to each other and solve for the final velocity:
mass_car1 * velocity_car1 + mass_car2 * velocity_car2 + mass_car3 * velocity_car3 + mass_car4 * velocity_car4 + mass_car5 * velocity_car5 = (mass_car1 + mass_car2 + mass_car3 + mass_car4 + mass_car5) * final_velocity
Once we have the final velocity, we can calculate the kinetic energy of the system using the formula mentioned in part (a):
Kinetic energy of all five cars after the collision = (1/2) * (mass_car1 + mass_car2 + mass_car3 + mass_car4 + mass_car5) * final_velocity^2
(c) Based on the information given, we can determine whether energy is conserved in this collision.
The energy is conserved if the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
If the calculated kinetic energy values from part (a) and part (b) are equal, then we can conclude that the energy is conserved. If they are not equal, then energy is not conserved.
Now, let's proceed with the calculations to find the answers.
To determine the kinetic energy of car 5 before the collision (question a), we can use the formula for kinetic energy: KE = (1/2)mv^2, where KE is the kinetic energy, m is the mass, and v is the velocity.
Given that the mass of car 5 is the same as the other four cars (11300 kg) and its velocity is 19.3 m/s, we can substitute these values into the formula:
KE = (1/2) * 11300 kg * (19.3 m/s)^2
= 11278.55 J
Therefore, the kinetic energy of car 5 before the collision is 11278.55 Joules.
To determine the kinetic energy of all five cars just after the collision (question b), we need to consider the conservation of kinetic energy. In an elastic collision, where there is no loss of kinetic energy, the total kinetic energy before the collision is equal to the total kinetic energy after the collision.
Since car 5 collides and couples with the other four cars, their final velocity will be the same. Let's call that velocity v_f.
To find the kinetic energy of all five cars just after the collision, we can use the same formula:
KE_total = (1/2) * (m1 + m2 + m3 + m4 + m5) * v_f^2
Given that the mass of each car is 11300 kg, we substitute these values into the formula:
KE_total = (1/2) * 11300 kg * (v_f)^2
Since v_f is the same for all five cars, we can simplify further:
KE_total = (1/2) * 11300 kg * v_f^2
Therefore, the kinetic energy of all five cars just after the collision is (1/2) * 11300 kg * v_f^2.
Now, to determine if energy is conserved in this collision (question c), we compare the kinetic energy of car 5 before the collision (part a) to the kinetic energy of all five cars just after the collision (part b).
If the two kinetic energies are equal, then energy is conserved. Therefore, we need to check if the equation from part a (11278.55 J) is equal to the equation from part b.
If the two equations are equal, we can conclude that the energy is conserved in the collision. If they are not equal, then the energy is not conserved.
In this case, as we don't have the value of the final velocity (v_f), we don't have sufficient information to determine if energy is conserved or not (answer choice 2: Insufficient information).