A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that μs\mu_{s} = 0.5 and μk\mu_{k} = 0.3. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.

Ch 06: Dynamics I: Motion Along a Line

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Knight Calc 5th Edition

Ch 06: Dynamics I: Motion Along a Line

문제 26b

6장, 문제 26b

A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that $μ_{s}$ = 0.5 and $μ_{k}$ = 0.3. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up.

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Start by identifying all the forces acting on the crate. These include the gravitational force (weight), the normal force, the frictional force, and any applied force due to the conveyor belt's motion.

Draw the free-body diagram. Represent the crate as a point or a small box. Draw a downward arrow labeled as the gravitational force $ F_g = m \cdot g $, where $ m = 10 \ \text{kg} $ and $ g = 9.8 \ \text{m/s}^2 $.

Draw an upward arrow of equal length to the gravitational force, labeled as the normal force $ F_N $. This force is exerted by the conveyor belt and balances the weight of the crate in the vertical direction.

Since the conveyor belt is speeding up, there is a tendency for the crate to resist this motion due to inertia. The frictional force acts to oppose this relative motion. Draw a horizontal arrow pointing in the direction of the conveyor belt's motion, labeled as the static frictional force $ F_{\text{friction}} $. The maximum static friction is given by $ F_{\text{friction}} = \mu_s \cdot F_N $, where $ \mu_s = 0.5 $.

Finally, ensure that the diagram is complete and consistent. Verify that all forces are labeled correctly and that the directions of the forces align with the physical situation described (e.g., friction opposes relative motion, normal force is perpendicular to the surface, and weight acts downward).

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주요 개념

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

Free-Body Diagram

A free-body diagram is a graphical representation used to visualize the forces acting on an object. It includes all the forces, such as gravitational force, normal force, frictional force, and any applied forces. In this scenario, the diagram will help identify how these forces interact when the conveyor belt accelerates.

Friction

Friction is the force that opposes the relative motion of two surfaces in contact. It is characterized by two coefficients: static friction (mu(s)), which prevents motion, and kinetic friction (mu(k)), which acts when the object is sliding. Understanding these coefficients is crucial for analyzing the forces on the crate as the conveyor belt speeds up.

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). This principle is essential for determining how the forces on the crate affect its motion, especially when the conveyor belt accelerates, leading to a net force that influences the crate's acceleration.