# Stability of a Vehicle on a Slope (Automobile)

31.9.

## Stability of a Vehicle on a Slope

Let the vehicle rest on a slope of inclination 0 to the horizontal. This alters the distribution of the weight between the front and back axle and gives rise to reaction which can have comĀ­ponents along the perpendicular to the inclined plane as shown in Fig. 31.8.
Now, resolving forces parallel and perpenĀ­dicular to the slope respectively,

Fig. 31.8. Force acting on a vehicle at rest on an inclined plane.

It should be noted that when the vehicle is being driven up, the angle of overturning is, in general, smaller than in the present case and also the condition of instability becomes different from those discussed above.
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Example 31.6. A vehicle of total weight 49050 N is held at rest on a slope of 10 . It has a wheel base of 2.25 m and its centre of gravity is 1.0 m in front of the rear axle and 1.5 m above the ground level. Find
(a) what are the normal reactions at the wheels ?
(6) assuming that sliding does not occur first, what will be the angle of slope so that the vehicle will overturn ?
(c) assuming all the wheels are to be braked, what will be the angle of the slope so that the vehicle will begin to slide if the coefficient of adhesion between the tyre and the ground is 0.35 ?

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