a locomotive pulls 10 identical freight cars. the force between the locomotive and the first car is 100,000 Newtons, and the acceleration of the train is 2m/s^2. there is no friction to consider.what is the force between the ninth and tenth cars?
Well, in this case, it seems like the force between the ninth and tenth cars would be... drumroll please... zero Newtons! Why? Because there is no friction to consider and the locomotive is the one doing all the hard work pulling the train. The force between the ninth and tenth cars would be like two shy clowns waving at each other from a distance – not really doing anything to affect each other.
To determine the force between the ninth and tenth cars, we need to consider the forces acting on the train and apply Newton's second law of motion.
According to Newton's second law, the force acting on an object is equal to its mass multiplied by its acceleration. In this case, the mass of the train is the sum of the masses of the locomotive and the 10 cars.
Since all the cars are identical, we can denote the mass of each car as "m". Therefore, the total mass of the train is:
Total mass = mass of locomotive + (mass of 10 cars)
Total mass = m + (10 * m)
Total mass = 11m
Now, we can calculate the net force acting on the train using Newton's second law:
Force = mass * acceleration
Force = (11m) * (2 m/s^2)
Force = 22m
Given that the force between the locomotive and the first car is 100,000 Newtons, we can set up the following equation:
100,000 N = 22m
To find the value of "m", we divide both sides of the equation by 22:
m = 100,000 N / 22
m ≈ 4,545.45 kg
Now, we can determine the force between the ninth and tenth cars. Since the ninth car experiences the same force as the locomotive, we have:
Force between ninth and tenth cars = 100,000 N
Therefore, the force between the ninth and tenth cars is 100,000 Newtons.
To find the force between the ninth and tenth cars, we need to consider Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = ma).
Since all the freight cars are identical, we can assume that the mass of each car is the same. Let's call this mass 'm'.
The force between the locomotive and the first car is given as 100,000 Newtons, so we can write this as:
100,000 N = m * 2 m/s^2
Now, to find the force between the ninth and tenth cars, we need to find the mass of the entire train first. Since the locomotive pulls 10 identical freight cars, the total mass of the train is equal to the mass of the locomotive plus the mass of all the cars.
So, the total mass of the train can be written as:
Mass of the train = Mass of the locomotive + (mass of each car * number of cars)
Since the mass of each car is 'm' and the number of cars is 10, we have:
Mass of the train = Mass of the locomotive + (m * 10)
Now, we can rewrite the force equation using the total mass of the train:
100,000 N = (Mass of the locomotive + (m * 10)) * 2 m/s^2
Simplifying the equation further:
100,000 N = Mass of the locomotive * 2 m/s^2 + (m * 10) * 2 m/s^2
Now, we have an equation with two unknowns: the mass of the locomotive and the mass of each freight car. Without additional information, we cannot solve for the force between the ninth and tenth cars.
F = m a
100,000 = m of ten * 2
m of ten = 50,000 kg
so
m of one = 5,000 kg
F = m a = 5,000 * 2 = 10,000 Newtons