what is the centripetal force of the train in the previous problem whose speed is 27.8 m/s rounding a curve whose radius of curvature is 150m if the train mass is 8000 kg
To find the centripetal force of the train, we will use the formula:
Fc = (m * v^2) / r,
Where Fc is the centripetal force, m is the mass of the train, v is the velocity of the train, and r is the radius of curvature.
In this case, we are given:
m = 8000 kg (mass of the train)
v = 27.8 m/s (speed of the train)
r = 150 m (radius of the curve)
Plugging these values into the formula, we get:
Fc = (8000 kg * (27.8 m/s)^2) / 150 m
To calculate this, we can follow these steps:
Step 1: Square the velocity
(27.8 m/s)^2 = 772.84 m^2/s^2
Step 2: Multiply the mass by the square of the velocity
8000 kg * 772.84 m^2/s^2 = 6182,720 kg·m^2/s^2
Step 3: Divide the result by the radius of curvature
6182,720 kg·m^2/s^2 / 150 m = 41,218.13 N (rounded to two decimal places)
Therefore, the centripetal force of the train is approximately 41,218.13 N.