Objects On a Slope

For an object on a slope inclined at θ to the horizontal, it helps to resolve its weight W into two components: Wsinθ acting down the slope and Wcosθ acting perpendicular to the slope.For a vehicle at rest on the slope, the support forces S₁ and S₂ on the wheels act perpendicular to the slope and balance the perpendicular component of the weight, S₁ + S₂ = Wcosθ. The friction force F acts up the slope and balances the component down the slope, F = Wsinθ.As the slope gets steeper, Wsinθ increases. If it becomes larger than the maximum friction the surface can provide, the object slides down the slope.An object can also topple. The weight acts through the centre of mass, and as long as its line of action passes inside the base, the weight gives a moment that returns the object to the slope. If the line of action falls outside the base, the moment turns it over. Tall, narrow objects with a high centre of mass topple at smaller angles.