Ch 06: Dynamics I: Motion Along a Line

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 06: Dynamics I: Motion Along a Line

문제 28

6장, 문제 28

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.

검증된 단계별 안내

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:

F

_g = mg, where

m

is the mass of the truck (4000 kg) and

g

is the acceleration due to gravity (9.8 m/s²).

Determine the component of the gravitational force parallel to the slope using the formula:

F

_parallel = F_g sin(θ), where

θ

is the angle of the slope (15 degrees).

Calculate the maximum static friction force using the formula:

F

_friction = μ_s F_normal, where

μ

_s is the coefficient of static friction (0.90) and

F

_normal is the normal force, calculated as

F

_g cos(θ).

Compare the parallel component of the gravitational force (

F

_parallel) with the maximum static friction force. If

F

_parallel is less than or equal to the maximum static friction force, the friction force equals

F

_parallel, as the truck does not slide.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

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.

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.