A 20,000 kg vehicle is running at 80km/hr in a rotonda with a radius of curvature 25m compute for the centripetal force
To compute the centripetal force, we can use the equation:
F = (m * v^2) / r
Where:
- F is the centripetal force
- m is the mass of the vehicle (20,000 kg)
- v is the velocity of the vehicle (80 km/hr)
- r is the radius of curvature of the roundabout (25 m)
First, we need to convert the velocity from km/hr to m/s:
1 km/hr = 1000 m/3600 s = 5/18 m/s
So, the velocity (v) in m/s is:
v = 80 * (5/18) m/s = 400/18 m/s ≈ 22.222 m/s (rounded to 3 decimal places)
Now, we can substitute the values into the formula:
F = (20,000 kg * (22.222 m/s)^2) / 25 m
Calculating the equation further:
F = (20,000 kg * 493.827 m^2/s^2) / 25 m
F ≈ (9,876,540 kg·m^2/s^2) / 25 m
F ≈ 394,061.6 N
Therefore, the centripetal force acting on the vehicle is approximately 394,061.6 Newtons.