A train with a mass of 120Mg accelerates uniformly on a horizontal track.the resistance to movement is 5N per KN of the mass of the train. The force in the draw-bar of the locomotive is 80KN.calculate: 1.the force required for the constant speed.
2.the force that causes the acceleration.
3.the acceleration
F=ma
F= 120×1000 × 1
=120000N
=120KN
1.3.1
1.The force required for the constant speed
2.The force that causes the acceleration
3.The acceleration
Calculate the force that causes the acceleration
To calculate the force required for constant speed, we need to find the force opposing the motion. In this case, the resistance to movement is given as 5N per KN of the mass of the train.
1. The force required for constant speed:
First, convert the mass of the train from Mg to kilograms:
120Mg = 120 x 1000 kg = 120,000 kg
Now, find the resistance force opposing the motion using the given resistance per mass:
Resistance force = (5 N/Kg) x (120,000 kg) = 600,000 N
Therefore, the force required for constant speed is 600,000 N.
2. The force that causes acceleration:
The force that causes acceleration is the difference between the force required for constant speed and the force in the draw-bar of the locomotive, which is given as 80 kN (kilonewtons).
Convert the force into Newtons:
80 kN = 80,000 N
Force causing acceleration = Force required for constant speed - Force in draw-bar
Force causing acceleration = 600,000 N - 80,000 N = 520,000 N
Therefore, the force that causes acceleration is 520,000 N.
3. The acceleration:
To calculate the acceleration, we can use Newton's second law of motion, which states that force is equal to mass multiplied by acceleration (F = m * a).
Rearranging the formula, we have:
Acceleration (a) = Force (F) / Mass (m)
Using the force causing acceleration calculated earlier and the given mass of the train:
Acceleration = 520,000 N / 120,000 kg = 4.33 m/s^2
Therefore, the acceleration of the train is 4.33 m/s^2.