The engine of a train has a mass of 5x10^4 kg. it can accelerate six railway cars having a total mass of 3x10^5 kg by 0.4 m/s^2 (the 6 railway cars have a combined mass of 3x10^5). what acceleration can the same engine using the same force give to four railway cars having a total mass of 2x10^5kg?
This question has been answered elsewhere by both BobPursley and myself
To solve this problem, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).
Given information:
- Mass of the engine: 5x10^4 kg
- Mass of the six railway cars: 3x10^5 kg
- Acceleration of the six railway cars: 0.4 m/s^2
- Mass of the four railway cars: 2x10^5 kg
First, let's find the total mass of the train for the first scenario (with six railway cars):
Total mass = Mass of the engine + Mass of the railway cars
Total mass = 5x10^4 kg + 3x10^5 kg
Total mass = 3.5x10^5 kg
Next, let's find the force applied in the first scenario:
Force = Total mass * Acceleration
Force = 3.5x10^5 kg * 0.4 m/s^2
Force = 1.4x10^5 N
Now, we can determine the acceleration for the second scenario (with four railway cars) using the same force:
Force = Mass of the train * Acceleration
1.4x10^5 N = (Mass of the engine + Mass of the four railway cars) * Acceleration
Since we know the total mass of the train for the second scenario is the mass of the engine plus the mass of the four railway cars, we can substitute this into the equation:
1.4x10^5 N = (5x10^4 kg + 2x10^5 kg) * Acceleration
1.4x10^5 N = 2.5x10^5 kg * Acceleration
Now, let's solve for the acceleration:
Acceleration = 1.4x10^5 N / 2.5x10^5 kg
Acceleration = 0.56 m/s^2
Therefore, the same engine using the same force can give a acceleration of 0.56 m/s^2 to four railway cars having a total mass of 2x10^5 kg.