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 the following
1. the force required for the constant speed.
2. the force that causes acceleration.
3. the acceleration
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, and the mass of the train is 120Mg (1 Mg = 1000 kg). So, the total resistance force can be calculated as follows:
Resistance force = (Resistance per kN) * (Mass of the train in kN)
Resistance force = 5N/kN * 120 M * 1000 kg/Mg
Resistance force = 5N/kN * 120 * 1000 * 1000 N
Resistance force = 600,000,000 N
Therefore, the force required for constant speed would be equal to the resistance force, which is 600,000,000 N.
To calculate the force that causes acceleration, we need to subtract the force required for constant speed from the force in the draw bar of the locomotive. Given that the force in the draw bar is 80 kN, we can calculate the force that causes acceleration as follows:
Force causing acceleration = Force in draw bar - Force required for constant speed
Force causing acceleration = 80 kN - 600,000,000 N
Note that we need to convert the force in the draw bar to Newtons by multiplying it by 1000:
Force causing acceleration = 80 kN - 600,000,000 N
Force causing acceleration = 80,000 N - 600,000,000 N
Force causing acceleration = -599,920,000 N
It is important to note that the negative sign indicates that the force causing acceleration is in the opposite direction of the applied force.
To calculate the acceleration, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration:
Net force = Mass * Acceleration
We can rearrange the formula to calculate the acceleration:
Acceleration = Net force / Mass
Since we already have the force causing acceleration (-599,920,000 N) and the mass of the train (120 Mg = 120 * 1000 kg), we can calculate the acceleration as follows:
Acceleration = (-599,920,000 N) / (120 * 1000 kg)
Acceleration = -4,999.33 m/s^2
The negative sign indicates that the train is decelerating or accelerating in the opposite direction of the applied force.