A railroad diesel engine weighs 3.9 times as much as a freight car. The diesel engine coasts at 5.3 km/h into the freight car that is initially at rest. After they couple together, what is their speed?
To find the final speed of the coupled diesel engine and freight car, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum of an isolated system remains constant before and after an event. In this case, the system consists of the diesel engine and the freight car.
The momentum of an object can be calculated by multiplying its mass by its velocity. So, let's assign variables to the given information:
Let the mass of the freight car be FC.
The weight of the diesel engine is 3.9 times the weight of the freight car, so the mass of the diesel engine can be written as 3.9 * FC.
The initial velocity of the diesel engine is 5.3 km/h, and the initial velocity of the freight car is 0 km/h because it is initially at rest. We'll convert the velocities to meters per second (m/s) since the units need to be consistent.
1 km/h = 1000 m/3600 s = 5/18 m/s
So, the initial velocity of the diesel engine (DV) is (5.3 x 5/18) m/s = 1.472 m/s, and the initial velocity of the freight car (FV) is 0 m/s.
According to the principle of conservation of momentum, the initial momentum of the system is equal to the final momentum of the system.
Initial momentum = Final momentum
(Mass of diesel engine x Velocity of diesel engine) + (Mass of freight car x Velocity of freight car)
= (Mass of diesel engine + Mass of freight car) x Final velocity
(3.9 x FC x 1.472 m/s) + (FC x 0 m/s) = (3.9 x FC + FC) x Final velocity
Since the freight car's initial velocity is zero, the equation simplifies to:
(3.9 x FC x 1.472 m/s) = (4.9 x FC) x Final velocity
Dividing both sides of the equation by FC and simplifying:
3.9 x 1.472 m/s = 4.9 x Final velocity
Final velocity = (3.9 x 1.472 m/s) / 4.9
Final velocity ≈ 1.172 m/s
So, the final speed of the coupled diesel engine and freight car is approximately 1.172 m/s.