A railroad car with a mass of 1.91 multiplied by 104 kg moving at 2.86 m/s joins with two railroad cars already joined together, each with the same mass as the single car and initially moving in the same direction at 1.40 m/s.
What is the speed of the three joined cars after the collision?
What is the decrease in kinetic energy during the collision?
conservation of momentum applies
Momentum before= momentum after
M*2.86+2M*1.40=3M*V
find V
How do you find the "decrease in kinetic energy during the collision?"
To find the speed of the three joined cars after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object can be calculated by multiplying its mass by its velocity. Let's denote the mass of each car as m and their initial velocities as v1, v2, and v3.
Before the collision:
The total momentum before the collision is the sum of the individual momenta of the three cars.
Total momentum before = (mass of car 1 * velocity of car 1) + (mass of car 2 * velocity of car 2) + (mass of car 3 * velocity of car 3)
= (m * 2.86 m/s) + (m * 1.40 m/s) + (m * 1.40 m/s)
= 2.86m + 1.40m + 1.40m
After the collision:
The final velocities of the three joined cars will be the same since they are now a single system. Let's denote the final velocity as Vf.
Total momentum after = (total mass of the three cars * final velocity)
= (3m) * Vf
According to the conservation of momentum principle:
Total momentum before = Total momentum after
2.86m + 1.40m + 1.40m = 3m * Vf
Simplifying the equation, we can solve for Vf:
5.66m = 3m * Vf
Dividing both sides of the equation by 3m, we get:
Vf = 5.66m / (3m) = 1.8867 m/s
So, the speed of the three joined cars after the collision is approximately 1.8867 m/s.
Now let's calculate the decrease in kinetic energy during the collision.
The kinetic energy of an object can be calculated using the formula:
Kinetic energy = 0.5 * mass * velocity^2
The decrease in kinetic energy is the difference between the kinetic energy before and after the collision.
Before the collision:
The total kinetic energy before the collision is the sum of the kinetic energies of the three individual cars.
Total kinetic energy before = (0.5 * mass of car 1 * (velocity of car 1)^2) + (0.5 * mass of car 2 * (velocity of car 2)^2) + (0.5 * mass of car 3 * (velocity of car 3)^2)
= (0.5 * m * (2.86 m/s)^2) + (0.5 * m * (1.40 m/s)^2) + (0.5 * m * (1.40 m/s)^2)
After the collision:
The total kinetic energy after the collision can be calculated using the formula with the final velocity (Vf) we found earlier.
Total kinetic energy after = 0.5 * (total mass of the three cars) * Vf^2
= 0.5 * (3m) * (1.8867 m/s)^2
The decrease in kinetic energy is the difference:
Decrease in kinetic energy = Total kinetic energy before - Total kinetic energy after
Simplifying the equation, we can find the decrease in kinetic energy.