Mechanical Engineering - Engineering Mechanics - Discussion

Three forces creating torques are affecting on the car in and make the car balanced without rolling. centrifugal force Fc wich depeds on the mass and velosity and radius of the curve. The other tow is the wieght (W) which depends on the mass and the gravitational accelleration and the spring force Fs (the car is suspended on the chasis via springs) whcih depends on the change in the height of the spring that proportional to tan($) ($) is the inclination angle. Putting all in equation.

Fc * h = W * n + Fs * x --------------(1)

Fc = Mass * V^2/R --------------(2)
W = Mass* G --------------------(3)
Fs = (Spring Constant c) * (Change in spring hight L) -------------(4)
(Change in spring hight L) is proportional to tan($) where $ is the inclination angle.

Then from equation (4):
Fs = c * c2 * tan($) ----------------(5)

Using Equations 1, 2, 3 & 5:

Mass * V^2/R * h = Mass * G * n + c * c2 * x * tan($)

Hence:
tan($) = Mass * (V^2/R * h - G * n) / ( c * c2 * x ) ---------------------(6)

So it is clear that the inclination angle depends on the mass and velocity of the car.

It depends.

As we know for a vehicle in a circular path, a centripetal force acts to which it tends to lean outward making an angle of contact with the road.

But this centripetal force resulting in load transfer, acts on the center of mass height (not just centre of mass) , therefore resulting in different lean angles for vehicles with the same height and different loads (mass).

If you tie a 5kg stone to a rope and swing it in a circular manner with a velocity of 5m/s observe the angle of inclination. Then try this experiment with a 10kg stone tied to the same rope and swing it with a velocity of 5m/s, you would observe that the angle of inclination is the same. i.e. the rope is tilted the same way in both experiments.

Since it is a vehicle on the ground there must be a consideration on frictional force. Due to that mass come into play by adding normal force to the surface. And due to centrifugal force (never mentioned in free space) that friction pushes away the body. So that the vehicle tend to get inclined and depends on mass certainly.

When vehicle moves in a circular path, a gyroscopic effect comes into action on the vehicle which try to make inner side of wheels up and try to rotate the car. But the gyroscopic effect depends upon speed of vehicle so the inclination will also depends upon the speed of vehicle.

When a car goes around a banked circular path, it's mass determines the force it feels due to the gravitational pull as well as the centrifugal force. Since it plays a factor in opposing forces and there is no other mass independent force, the mass term gets cancelled out.

Actually there is no need to consider mass into account when body rotates in circular path because when it rotates in circular path the concentration of mass is at the centre of the rotating body. Only tangential force is come into account.

Don't complicate,

Imagine your driving a bike in circular path.

Now imagine your driving a cycle in circular path.

The mass of bike is more than mass of cycle but both of them incline in certain angle.

It is not.

1). Gyroscopic principle. It is centrifugal action.
2). Body don't move downwards, it will move inwards.
3). Relation is-tan$=v2/rg.
4). Question is angle of inclination with horizontal.

Acceleration for a circular motion is v^2/r, so not dependent on mass. Acceleration from gravity isn't either. The angle is just the angle of the vector sum of these two accelerations.