Mechanical Engineering - Engineering Mechanics - Discussion

Angle of inclination depends solely on the radius of curvature of path.

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.

A common eg : Mout ka Kuan (Well of Death).

Car and bike both rotate in the speed are same.

But the mass of the car is greater than the bike.

B'coz It only depends on speed.

Tan$ = v square/rg,
Where, v = velocity, g = gravity. So there is no depandent in mass.

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.

It depends on velocity of the vehicle.

In case, if the angle of inclination of the vehicle.

I think mass of vehicle doesn't matter if it is moving in circular path because it's depends on speed of vehicle.

Because of object moved on circular path.
So equation of angle is,
Angle = w*t.
So does not depend on mass.

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).

We have the relation that tan@=v2/rg.