an automobile of mass 1800kg takes a turn of radius 270m. If the force on the tyres to maintain the motion along the curve is not to exceed 630n, the limiting speed of the vehicle assuming no banking will be
To determine the limiting speed of the vehicle, we need to consider the maximum force that the tires can exert to maintain the motion along the curve.
First, let's calculate the maximum velocity at which the force on the tires exceeds the given limit. This force is equal to the centripetal force required to keep the vehicle in a circular motion.
The centripetal force can be calculated using the formula:
F = (mv^2) / r
Where:
F is the centripetal force,
m is the mass of the vehicle,
v is the velocity,
and r is the radius of the curve.
We need to rearrange the formula to solve for velocity (v):
v = √((Fr) / m)
Substituting the given values:
F = 630 N,
m = 1800 kg,
r = 270 m
v = √((630 N * 270 m) / 1800 kg)
Calculating this expression:
v = √(94500 Nm / 1800 kg)
v = √(52.5 m^2/s^2)
v ≈ 7.24 m/s
Therefore, the limiting speed of the vehicle, assuming no banking, is approximately 7.24 m/s.