A train consists of 40 freight cars, each having a mass of 2.71 × 105 kg. If the engine (which has twice the mass of a freight car) exerts a net force of +1.12 × 105 N, what will be the acceleration of this train?
F=(40•m+2•m)a
a=F/42m
To find the acceleration of the train, we can use Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = m * a).
In this case, the force acting on the train is the net force exerted by the engine, which is +1.12 × 10^5 N.
The mass of the train can be calculated by adding up the masses of all the freight cars and the engine. Since the mass of each freight car is 2.71 × 10^5 kg and there are 40 of them, the total mass of the freight cars is:
40 cars * 2.71 × 10^5 kg/car = 1.08 × 10^7 kg.
The mass of the engine is twice the mass of a freight car, so:
mass of the engine = 2 * 2.71 × 10^5 kg = 5.42 × 10^5 kg.
Hence, the total mass of the train is:
mass of the train = mass of the freight cars + mass of the engine
= 1.08 × 10^7 kg + 5.42 × 10^5 kg
= 1.13 × 10^7 kg.
Now, we can use Newton's second law to find the acceleration:
F = m * a
1.12 × 10^5 N = 1.13 × 10^7 kg * a
Solving for the acceleration (a), we have:
a = (1.12 × 10^5 N) / (1.13 × 10^7 kg)
= 0.00991 m/s^2
Therefore, the acceleration of this train is approximately 0.00991 m/s^2.