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7. Friction, Inclines, Systems
Inclined Planes
Problem 28
Textbook Question
A 4000 kg truck is parked on a 15° slope. How big is the friction force on the truck? The coefficient of static friction between the tires and the road is 0.90.

1
Identify the forces acting on the truck: The truck is subject to gravitational force, normal force, and static friction. The gravitational force can be broken into two components: one parallel to the slope (causing the truck to slide down) and one perpendicular to the slope (contributing to the normal force).
Calculate the gravitational force acting on the truck using the formula: , where is the mass of the truck (4000 kg) and is the acceleration due to gravity (9.8 m/s²).
Determine the component of the gravitational force parallel to the slope using the formula: , where is the angle of the slope (15 degrees).
Calculate the maximum static friction force using the formula: , where is the coefficient of static friction (0.90) and is the normal force, calculated as .
Compare the parallel component of the gravitational force () with the maximum static friction force. If is less than or equal to the maximum static friction force, the friction force equals , as the truck does not slide.

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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Static Friction
Static friction is the force that resists the initiation of sliding motion between two surfaces in contact. It acts parallel to the surfaces and is dependent on the normal force and the coefficient of static friction. The maximum static friction force can be calculated using the formula: F_friction = μ_s * N, where μ_s is the coefficient of static friction and N is the normal force.
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Static Friction & Equilibrium
Normal Force
The normal force is the perpendicular force exerted by a surface to support the weight of an object resting on it. On an inclined plane, the normal force is less than the object's weight and can be calculated using the formula: N = mg * cos(θ), where m is the mass, g is the acceleration due to gravity, and θ is the angle of the incline. This force is crucial for determining the frictional force acting on the truck.
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The Normal Force
Inclined Plane
An inclined plane is a flat surface tilted at an angle to the horizontal, which affects the forces acting on an object resting on it. The angle of the incline influences both the normal force and the gravitational force components acting on the object. Understanding how to resolve these forces is essential for calculating the friction force and analyzing the object's stability on the slope.
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Intro to Inclined Planes
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Related Practice
Multiple Choice
A 5.0-kg box slides on the surface of a ramp that rises at 37° above the horizontal. The coefficient of kinetic friction between the box and the surface of the ramp is 0.60. What is the magnitude of the acceleration of the box as it slides down the ramp?
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