What is the centripetal force on a vehicle rounding a circular curve with a radius of 80m at a constant speed of 90 km/h if the vehicles mass is 2,000 kg? (Hint: first express the velocity in meters per second)
A: 20,250 N
B: 703 N
C: 625 N
D: 15,625 N
To find the centripetal force, we can use the formula:
F = (m * v^2) / r
Where:
- F is the centripetal force
- m is the mass of the vehicle
- v is the velocity of the vehicle
- r is the radius of the curve
First, we need to convert the velocity from km/h to m/s. To do this, we use the conversion factor 1 km/h = 0.27778 m/s.
So, v = 90 km/h × 0.27778 m/s = 25 m/s.
Now we can plug the values into the formula:
F = (2,000 kg * 25 m/s^2) / 80 m
F = 50,000 N / 80 m
F = 625 N
Therefore, the correct answer is option C: 625 N.