A railroad car with a mass of 2.33 × 104 kg moving at 3.71 m/s collides and 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 1.44 m/s.What is the final speed of the three joined cars after the collision?
Answer in units of m/s.
conservation of momentum
initial momentum=finalmomentum
2.33E4*3.71+(2*2.33E4)( 1.44)=2.33E4*3V
or
3.71+2.88=3v
solve for V
To find the final speed of the three joined railroad cars after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
The momentum of an object is given by the product of its mass and velocity. So, let's calculate the initial momentum and final momentum separately and equate them.
The initial momentum of the first railroad car is given by the product of its mass (2.33 × 10^4 kg) and velocity (3.71 m/s):
Initial momentum of the first car = (2.33 × 10^4 kg) × (3.71 m/s)
The initial momentum of the two already joined cars is given by the product of their combined mass (2 × 2.33 × 10^4 kg) and velocity (1.44 m/s):
Initial momentum of the two cars = (2 × 2.33 × 10^4 kg) × (1.44 m/s)
Now, let's find the final momentum of the three joined cars after the collision. Since they become one object and move together, their final mass will be the sum of the masses of the initial three cars.
The final momentum will be the product of the final mass and final velocity, which we need to find:
Final momentum of the three cars = (total mass) × (final velocity)
Now, according to the principle of conservation of momentum, we can equate the initial momentum to the final momentum:
Initial momentum of the first car + Initial momentum of the two cars = Final momentum of the three cars
(2.33 × 10^4 kg) × (3.71 m/s) + (2 × 2.33 × 10^4 kg) × (1.44 m/s) = (total mass) × (final velocity)
Now, let's calculate the final velocity by rearranging the equation:
(final velocity) = [ (2.33 × 10^4 kg) × (3.71 m/s) + (2 × 2.33 × 10^4 kg) × (1.44 m/s) ] / (total mass)
Substituting the values given,
(final velocity) = [ (2.33 × 10^4 kg) × (3.71 m/s) + (2 × 2.33 × 10^4 kg) × (1.44 m/s) ] / [(2.33 × 10^4 kg) + (2 × 2.33 × 10^4 kg)]
Calculating this equation will give us the final velocity of the three joined cars after the collision.