A 48,000 -pound truck is parked on a 10^∘ slope (see figure). Assume the only force to overcome

step 1 So for this problem, we know that a 48 ,000 pound truck is parked on a 10 degree slope. Assuming

A 48,000 -pound truck is parked on a 10^∘ slope (see...

A 48,000 -pound truck is parked on a $10^{\circ}$ slope (see figure). Assume the only force to overcome is that due to gravity. Find (a) the force required to keep the truck from rolling down the hill and (b) the force perpendicular to the hill.

Key Concepts

Component of Weight Parallel to the Incline

This component, typically calculated as the weight multiplied by the sine of the incline angle, represents the force acting along the slope. It is crucial in determining the threshold force needed to prevent the object from sliding down the incline.

Component of Weight Perpendicular to the Incline

This component is obtained by multiplying the weight by the cosine of the inclining angle and represents the force pressing the object into the surface. It plays an essential role in calculating the normal force, which is important for understanding the frictional forces between the object and the surface.

Inclined Plane Analysis

This concept involves examining the forces acting on an object placed on a sloped surface. The analysis specifically requires resolving the gravitational force into components that are parallel and perpendicular to the incline, which helps in understanding the object's potential motion or static equilibrium on the slope.

Decomposition of Forces

This fundamental technique in physics involves breaking down a force vector into its orthogonal components using trigonometric functions. In the context of an inclined plane, the weight of an object is typically decomposed into two components: one parallel to the plane (which might cause the object to slide down) and one perpendicular to the plane (which determines the normal force).

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