Simpler version:
An automobile with a mass of 2000kg is traveling at a constant speed of 36km/h on a horizontal road with a slope of 5%. What is the maximum turning radius before the car flips over? Assume a wheelbase of 1.4m, a center of gravity height of 0.5m, a coefficient of friction between the wheels and the road of 0.5, and a gravitational acceleration of 10m/s^2.
Maximum turning radius = (36 km/h)^2 / (10 m/s^2 * tan(5%)) = 105.6 m
Same version:
A car weighing 2000kg is making a uniform turn on a road with a 5% slope at a constant speed of 36km/h. What is the radius of the turn at which the car will start to tip over? Assume a wheelbase of 1.4m, a center of gravity height of 0.5m, a coefficient of friction between the wheels and the road of 0.5, and a gravitational acceleration of 10m/s^2.
Maximum turning radius = (36 km/h)^2 / (10 m/s^2 * tan(5%)) = 105.6 m
More complex version:
A car with a mass of 2000kg is traveling at a constant speed of 36km/h on a horizontal road with a slope of 5%. The car is making a uniform turn and we want to determine the maximum turning radius before the car flips over. To solve this problem, we need to consider several factors.
First, we need to calculate the gravitational force acting on the car. The gravitational acceleration is approximately 10m/s^2, so the force of gravity on the car is:
Fgravity = m * g = 2000kg * 10m/s^2 = 20,000N
Next, we need to calculate the centripetal force required to keep the car in the turn. The centripetal force is given by:
Fcentripetal = m * v^2 / R
where m is the mass of the car, v is the speed of the car, and R is the radius of the turn.
To determine the maximum turning radius before the car flips over, we need to find the point at which the centripetal force equals the force of gravity:
Fcentripetal = Fgravity
m * v^2 / R = m * g
R = v^2 / (g * tanθ)
where θ is the slope of the road.
Plugging in the given values, we get:
R = (36 km/h)^2 / (10 m/s^2 * tan(5%)) = 105.6 m
Finally, we need to calculate the maximum angle of inclination at which the car can make the turn without flipping over. This angle is given by:
α = arctan(h/B)
where h is the height of the car’s center of gravity and B is the wheelbase.
Plugging in the given values, we get:
α = arctan(0.5/1.4) = 20.56°
The maximum turning radius before the car flips over is therefore:
RL = R * sinα = 105.6 m * sin(20.56°) = 37.5 m
In conclusion, the maximum turning radius before the car flips over is 37.5m.
