A train with 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 locomotive is 80kN
Calculate
a. The force required for constant speed
b. The force that causes the acceleration
c. The acceleration
To calculate the force required for constant speed, we need to find the total resistance to movement. The resistance is given as 5N per kN of the train's mass, which means for a 120mg (0.12g) train, the resistance is:
Resistance = 5N/kN * 0.12g = 0.6N
Therefore, the force required for constant speed is equal to the resistance, which is 0.6N.
To calculate the force that causes the acceleration, we subtract the force required for constant speed from the force in the draw-bar locomotive:
Force causing acceleration = Force in draw-bar locomotive - Force required for constant speed
= 80kN - 0.6N (converting kN to N)
= 80,000N - 0.6N
= 79,999.4N
Therefore, the force that causes the acceleration is approximately 79,999.4N.
To calculate the acceleration, we can use Newton's second law of motion:
Force = mass * acceleration
Rearranging the formula, we get:
Acceleration = Force / mass
Given that the mass of the train is 120mg (0.12g), we need to convert it to kilograms:
Mass = 0.12g / 1000 (converting mg to kg)
= 0.00012kg
Using the force that causes acceleration calculated above, we have:
Acceleration = 79,999.4N / 0.00012kg
= 666,661,666.67 m/s^2
Therefore, the acceleration of the train is approximately 666,661,666.67 m/s^2.
To calculate the force required for constant speed, we need to consider the resistance to movement. The resistance to movement is given as 5N per kN of the mass of the train.
a. The force required for constant speed is equal to the resistance force.
To calculate the resistance force, we need to convert the mass of the train from milligrams (mg) to kilograms (kg), using the conversion factor of 1 mg = 1e-6 kg.
Mass of the train = 120 mg = 120 * 1e-6 kg = 0.00012 kg
Resistance force = 5 N/kN * 0.00012 kg = 0.0006 N
Therefore, the force required for constant speed is 0.0006 N.
b. The force that causes the acceleration can be calculated using Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma).
In this case, the force causing the acceleration is the force in the draw-bar locomotive, which is given as 80 kN.
However, we also need to convert the force from kilonewtons (kN) to newtons (N), using the conversion factor of 1 kN = 1000 N.
Force causing acceleration = 80 kN * 1000 N/kN = 80000 N
Therefore, the force that causes the acceleration is 80000 N.
c. The acceleration can be calculated using the formula:
acceleration = force causing acceleration / mass of the train
acceleration = 80000 N / 0.00012 kg = 666,666.67 m/s^2 (approximately)
Therefore, the acceleration is 666,666.67 m/s^2 (approximately).