Train cars are coupled together by being bumped into one another. Suppose two loaded train cars are moving toward one another, the first having a mass of 180,000 kg and a velocity of 0.300 m/s, and the second having a mass of 95,000 kg and a velocity of -0.120 m/s. (The minus indicates direction of motion.) What is their final velocity?
0.122 m/s
To find the final velocity of the train cars, 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, assuming there is no external force.
The momentum of an object is calculated by multiplying its mass by its velocity. Mathematically, momentum (p) is given by:
p = m * v
where:
p = momentum
m = mass of the object
v = velocity of the object
In this case, we have two train cars moving towards each other. The first train car has a mass of 180,000 kg and a velocity of 0.300 m/s, while the second train car has a mass of 95,000 kg and a velocity of -0.120 m/s.
The total initial momentum before the collision can be calculated by summing the individual momenta of the two train cars:
initial momentum = (mass of first car * velocity of first car) + (mass of second car * velocity of second car)
initial momentum = (180000 kg * 0.300 m/s) + (95000 kg * -0.120 m/s)
Next, we calculate the total mass of the train cars by summing their individual masses:
total mass = mass of first car + mass of second car
total mass = 180000 kg + 95000 kg
Now, we can find the final velocity by dividing the initial momentum by the total mass:
final velocity = initial momentum / total mass
Plug in the calculated values to get the final result.