A locomotive is pulling 17 freight cars, each of which is loaded with the same amount of weight. The mass of each freight car (with its load) is 37,000 kg. If the train is accelerating at 0.7 m/s2 on a level track, what is the tension in the coupling between the second and third cars? (The car nearest the locomotive is counted as the first car, and friction is negligible.)
The tension between cars 2 and 3 accelerates cars 3 through 17. That is a total of 15 cars.
F = M*a, with M = 15*37,000 = 555*10^3 kg
a = 0.7 m/s^2
Solve for F, in Newtons
388500
To find the tension in the coupling between the second and third cars, we can use Newton's second law of motion and apply it to the system. The net force acting on the second car is the tension in the coupling between the second and third cars, minus the force of friction.
Step 1: Find the total mass of the train
Since each freight car (with its load) has a mass of 37,000 kg, and there are 17 freight cars, the total mass of the train is:
Total mass = 37,000 kg x 17 = 629,000 kg
Step 2: Calculate the total force acting on the train
According to Newton's second law, the total force acting on an object is equal to its mass multiplied by its acceleration:
Total force = mass x acceleration
Total force = 629,000 kg x 0.7 m/s^2
Total force = 440,300 N
Step 3: Calculate the force of friction
Since friction is negligible, we can assume that the force of friction is zero.
Step 4: Calculate the tension in the coupling between the second and third cars
To find the tension, we subtract the force of friction from the total force:
Tension = Total force - Force of friction
Tension = 440,300 N - 0 N
Tension = 440,300 N
Therefore, the tension in the coupling between the second and third cars is 440,300 N.
To determine the tension in the coupling between the second and third cars, we need to understand the forces acting on the system.
First, let's consider the overall system. The locomotive is pulling the entire train, so the force exerted by the locomotive on the entire train is equal to the total mass of the train multiplied by its acceleration.
The total mass of the train is the sum of the mass of the locomotive and the mass of the 17 freight cars. Since each freight car weighs 37,000 kg, the total mass of the freight cars is 17 multiplied by 37,000 kg.
Next, we need to determine the force acting on the second car due to the third car. Assuming there is no slippage or stretching along the coupling, the force acting on the second car is exactly equal and opposite to the force acting on the third car.
Therefore, the force acting on the second car due to the third car is the same as the tension in the coupling between them.
To calculate this force, we can use Newton's second law of motion, F = ma. Rearranging the equation, we have F = m × a, where F is the force, m is the mass, and a is the acceleration.
In this case, the mass is the mass of a single freight car with its load (37,000 kg), and the acceleration is the acceleration of the train (0.7 m/s^2).
So, the tension in the coupling between the second and third cars is given by T = m × a, where T is the tension, m is the mass of a single freight car, and a is the acceleration.
Substituting the values into the formula, T = 37,000 kg × 0.7 m/s^2.
Calculating this will give us the tension in the coupling between the second and third cars.