A heavy freight train has a mass of 13200 metric tons. If the locomotive can pull with a force of 755000N, how long does it take to increase it's speed from 0 to 95.5 km/h?
To calculate the time it takes for the train to increase its speed from 0 to 95.5 km/h, we can use Newton's second law of motion:
Force = (mass) x (acceleration)
In this case, we need to find the acceleration of the train. The formula to convert speed from km/h to m/s is:
acceleration (in m/s^2) = (speed in km/h) x (1000 m) / (3600 s)
So, let's calculate the acceleration:
acceleration = (95.5 km/h) x (1000 m) / (3600 s)
= 26.5278 m/s^2
Now, we have the mass of the train (13200 metric tons) and the acceleration (26.5278 m/s^2). We can use the formula again to find the force:
Force = (mass) x (acceleration)
= (13200 metric tons) x (1000 kg/ton) x (9.8 m/s^2)
= 1293600000 N
Since the force that the locomotive can pull is 755000N, it's not enough to accelerate the train to the desired speed. Therefore, we need to calculate the additional force required.
Additional force = (force required to accelerate) - (force locomotive can pull)
= (1293600000 N) - (755000 N)
= 1292845000 N
Now that we have the additional force required, we can calculate the time using Newton's second law of motion:
Force = (mass) x (acceleration)
Time = Force / (additional force)
= (1292845000 N) / (755000N)
≈ 1711.4 seconds
So, it would take approximately 1711.4 seconds to increase the train's speed from 0 to 95.5 km/h, assuming the locomotive can pull with a force of 755000N.