A semi- trailer truck (seen from back) of mass M is negotiating a right hand curve on a level highway, The constant speed of the truck is v and the radius of curvature of it's circular trajectory is R. The road exerts normal forces on the trucks tires F1, F2 and a horizontal static friction force on each tire f1, f2 directed toward the centre of the curve. The trucks centre of mass is a height H above the road and the distance between the tires is W.
Apply newtons second law(s) in the non- inertial frame moving with the truck to find the magnitudes of the normal forces on terms of M,g,v,R,W. Assume the truck can be treated as a lamina lying in the plane of the page.
These equations will be needed for the solution:
F1 + F2 = Mg (vertical force balance)
MV^2/R * H + M g W/2 - F2*W = 0 (moment balance about the F1 tire)
f1 + f2 = M V^2/R (horizontal force balance)
I don't see how to solve for f1 and f2 separately if the tires are not skidding. F1 and F2 can be separately solved, but the f's do not have to be proportional to F when not skidding
To find the magnitudes of the normal forces on the tires, we can start by considering the forces acting on the truck in the non-inertial frame moving with the truck.
In the non-inertial frame, there are two main forces acting on the truck: the weight force (mg) and the centripetal force (mv^2 / R). The weight force acts vertically downward and has a magnitude of Mg, where M is the mass of the truck and g is the acceleration due to gravity.
The centripetal force acts horizontally towards the center of the curve and has a magnitude of Mv^2 / R, where v is the constant speed of the truck and R is the radius of curvature of its trajectory.
Since the truck is on a level highway, the normal forces exerted by the road on the tires (F1 and F2) are perpendicular to the road surface. These forces contribute to balancing the weight force and the centripetal force.
Given that the center of mass of the truck is at a height H above the road and the distance between the tires is W, we can draw a free-body diagram of the truck in the non-inertial frame.
From the diagram, we can observe that the vertical components of the normal forces, F1 and F2, must balance the weight force Mg. Therefore, F1 + F2 = Mg.
We can also observe that the horizontal components of the normal forces, F1 and F2, must balance the centripetal force Mv^2 / R. Therefore, F1 = F2 = Mv^2 / (2R).
Hence, in terms of M, g, v, R, and W, the magnitudes of the normal forces on the tires are:
F1 = F2 = Mv^2 / (2R)
F1 + F2 = Mg
Please note that these equations assume that the truck can be treated as a lamina lying in the plane of the page and neglect any other forces or complexities that may exist in a real-world scenario.