Name: calculating force moments in problem solving
Uploaded: 2023-09-22T11:49:20.000Z
Duration: 1 min 29 s
Channel: JoVE

考虑一名男子使用撬棍从木墙中拔出一枚钉子。撬棍在点 A 处与墙面接触。该男子在撬棍手柄处施加一个垂直向下的力 F1，而在爪部需要施加一个力 F2 才能将钉子拔出。确定该男子将钉子拔出所需的最小作用力。
在点 A，力 F1 所产生的力矩可表示为力的大小与其垂直距离乘积之和。代入数值后，可确定由 F1 在点 A 处产生的力矩。
类似地，将作用在钳爪上的力 F2 分解为分量后，可利用 F2 的正弦分量来确定 F2 在 A 点产生的力矩。
由于力矩的作用，F1 小于 F2，因此力 F1 不足以拔出钉子。
通过比较力矩方程并代入数值，可确定拔出钉子所需的最小力。

<ol>
	<li>罗素 C. 希伯勒。（2016）. 工程力学:静力学与动力学。皮尔森。页码 - 121-124。</li>
</ol>

力矩：问题解决

对力矩的标量表达式进行理解，并通过求解问题来正确的应用它，对于机械系统中的设计和分析至关重要。以下是使用力矩进行求解问题的步骤： <ol> <li>绘制系统的受力分析图（FBD）。受力分析图是对问题最基本的解决步骤。它是对作用在系统上所有作用力的图来进行表示。同时必须确定系统中所有的作用力，并且将它们包括在受力分析图中。</li> <li>确定计算力矩的轴线或点。在某些情况下，已经提供了需要计算净力矩的轴线或点。然而，在其他情况下，需要对问题来选择一个合适的轴线或点。</li> <li>计算力和轴线或点之间的垂直距离。垂直距离是力和所选的轴线或点之间的最短距离。</li> <li>计算每个力的力矩。在这一步骤中，将个别力的大小和它们所选的轴线或点的距离进行相乘，以此来计算它们的力矩。在这里，力矩是一个矢量，其方向垂直于力和所选的轴线或点的平面。</li> <li>求和力矩。一旦计算出所有力的力矩，必须对其进行代数求和，以此来获得作用在系统上的净力矩。</li> <li>确定净力矩的效应。如果净力矩为零，则不会进行旋转。如果净力矩为负，则物体将会进行顺时针旋转，如果净力矩为正，则物体将会进行逆时针旋转。</li> <li>求解问题。求解问题的最后一步是使用通过计算得出的净力矩来解决其给定的问题。例如，如果需要计算物体的角加速度，则可以将作用在物体上的净力矩与物体的转动惯量进行相除来得出。</li> </ol>

理解力矩的标量表达形式，并通过解题正确应用，对于设计和分析...至关重要

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Force System Resultants

力系合力

KEY TERMS AND CONCEPTS

关键术语与概念

Moment of a Force: Problem Solving

calculating force moments in problem solving

Calculating force moments in problem solving helps students analyze rotation in mechanical systems. The scalar form of the moment of a force is used to work through these problems step by step.

Start by drawing a free-body diagram, or FBD. An FBD is a sketch that shows every force acting on the system. Each force must be identified and included.

Next, identify the axis or point about which the moment is calculated. In some problems, that axis or point is given. In other cases, you must choose a suitable one. Then find the perpendicular distance, which is the shortest distance between the force and the axis or point.

After that, calculate the moment of each force. This is done by multiplying the force magnitude by its perpendicular distance. The moment is a vector quantity, and its direction is perpendicular to the plane of the force and the chosen axis or point.

Add the moments algebraically to find the net moment. Then interpret the result. If the net moment is zero, there is no rotational motion. If it is negative, the object rotates clockwise. If it is positive, the object rotates counterclockwise.

Use the net moment to solve the problem. For example, if angular acceleration is needed, divide the net moment by the moment of inertia of the object.

Calculating Force Moments in Problem Solving

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moment of a force: scalar formulation

Torque on a Flywheel: Direction and Size

Torque, or the moment of a force, describes how a force can make an object turn about an axis. It is a vector quantity, so it has both size and direction. This idea is important in physics, mechanics, and engineering. A simple flywheel example shows how torque works. The flywheel rotates about point O when a force is applied to it. The moment arm is the perpendicular distance from point O to the line of action of the force. The moment, in newton-meter (N-m), is found by multiplying the force...

moment of a force: problem solving

Calculating force moments in problem solving helps students analyze rotation in mechanical systems. The scalar form of the moment of a force is used to work through these problems step by step. Start by drawing a free-body diagram, or FBD. An FBD is a sketch that shows every force acting on the system. Each force must be identified and included. Next, identify the axis or point about which the moment is calculated. In some problems, that axis or point is given. In other cases, you must choose...

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Net Moment Sign Convention in 2D Forces

Net moment in two-dimensional force systems shows how multiple forces can cause rotation about a fixed point. The scalar formulation helps analyze equilibrium in structures that are acted on by several forces. It focuses on the x-y plane and uses a simple sign rule to describe the direction of rotation. To find the resultant moment, the moments from all forces in the system are considered about a chosen point A. Each moment is assigned a sign based on its sense of rotation. Positive moments...

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Moment of Force and Direction Rules

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cartesian form for vector formulation

Calculating Moment with Cartesian Vectors

Calculating moment with Cartesian vectors shows how position and force vectors work together. The moment of force is the cross product of these vectors, so it is a vector quantity. In Cartesian form, unit vectors help write the vectors in component form. The cross product can be arranged in determinant form. That determinant is then expanded to find the Cartesian vector form of the moment of force. This method gives a clear way to work through the calculation step by step. A revolving door...

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Resultant moment describes the total turning effect of multiple forces acting on an object. It shows how several forces can combine to make a body rotate about a point. In physics, moment is the tendency of a force to cause rotation. The resultant moment of a force system is a vector quantity. That means it can be added and subtracted like other vectors. For a system with two forces, F1 and F2, acting on a pole at points A and B, the resultant moment is written as MR = (rA x F1) + (rB x F2).

principle of moments

Resolving Forces in Moment Calculations

The principle of moments, also called Varignon's theorem, explains how a force creates rotation about a point. It is a key idea in physics and engineering. It also helps describe when a rigid body stays in equilibrium under external forces. The moment of a force is found by multiplying the force by the perpendicular distance from the point of application to the point being studied. A larger force or a larger distance gives a larger moment. This makes the idea useful for checking how strongly a...

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Torque About an Axis in 3D Systems

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Bicycle Torque and Moment About an Axis

The moment of a force about an axis describes how a force can make an object turn around a fixed line. In scalar analysis, the moment is found from the perpendicular distance between the axis of rotation and the line of action of the force. That distance is called the moment arm. A bicycle gives a clear example of this idea. When the cyclist pushes on the pedal, the chain applies a force to the wheel’s axle and makes it rotate. The axis of rotation passes through the axle, and the moment arm...

moment of a force about an axis: vector

Torque on a Bicycle Wheel: Vector Method

Torque, or the moment of a force, explains how a force can make an object rotate about an axis. A bicycle is a clear example. When a cyclist presses on the pedal, the crankshaft turns and helps drive the wheel. To analyze this motion, a coordinate system is set up first. The x-axis is tangential to the wheel, the y-axis is perpendicular to the x-axis and points upward, and the z-axis points outward from the wheel. In this setup, the force on the wheel axle lies along the x-axis. The axle...

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Couple Moments and the Right-Hand Rule

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Equivalent Couples in Mechanical Systems

Equivalent couples in mechanical systems describe pairs of forces that create the same rotational effect on a rigid body. Two couples are equivalent when they have the same moment magnitude and act in the same direction. They then cause the same angular displacement or angular acceleration in the body. A couple is made of equal and opposite forces separated by a perpendicular distance. The moment of the couple depends on both the force size and the spacing between the forces. For example, one...

moment of a couple: problem solving

Torque from a Couple: Solving Forces

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Equivalent Force and Moment Systems

Structural systems often experience several forces and couple moments at the same time. Engineers simplify these loading cases by replacing them with an equivalent force and moment system at a chosen point O. This makes the analysis easier while keeping the same external effects on the member. A key idea in this process is the principle of transmissibility. A force is a sliding vector, which means it can be moved anywhere along its line of action without changing how the body behaves...

simplification of a force and couple system i

simplification-of-a-force-and-couple-system-i

Resultant Forces in Force and Couple Systems

Force and couple systems can be reduced to a simpler equivalent system. This makes rigid body analysis easier because the external effect of the forces is captured with fewer elements. When the resultant force and resultant couple moment have perpendicular lines of action, the system may be reduced further to a single resultant force along a new line of action. Three common force systems can be simplified this way: concurrent, coplanar, and parallel. A concurrent force system has lines of...

simplification of a force and couple system: ii

simplification-of-a-force-and-couple-system-ii

Resultant Force and Wrench Motion

Resultant force and resultant couple moment describe how several forces and moments act together on a rigid body in three dimensions. When many forces act on an object, they can be replaced by one equivalent force. The moments from those forces can also be combined into one equivalent couple moment. In some cases, the resultant force and the resultant couple moment are not mutually perpendicular. That means the angle between them is not 90 degrees. To study this situation, the couple moment is...

distributed loads

Load Distribution on Shelves and Dams

Load distribution helps engineers describe how force spreads across a surface or structure. A distributed load is a continuous force per unit area, rather than a single point force. It is a common idea in many practical situations. A bookshelf full of stacked books is one simple example. The weight of the books is spread along the shelf, so the pressure changes across the surface. This pressure is measured in Newtons per square meter, or Pascals. A hydroelectric dam gives another clear...

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Finding Resultant Loads on a Beam

Structural engineering often requires finding the resultant load on a beam with changing force patterns. Here, a beam of length L carries a varying load made from parabolic and trapezoidal load distributions along the x-axis. The goal is to find the total load, where it acts, and the centroid of the combined area so the beam’s response can be predicted. The parabolic load is handled first. A small force element, dR, acts over a short distance, dx, and these elements are integrated across the...

distributed loads: problem solving

Equivalent Resultant Loads on Beams

Equivalent resultant loads on beams can be found by breaking a distributed load into smaller regions. This makes the beam easier to analyze. Each region can then be handled on its own before the results are combined. The magnitude of the equivalent resultant load for each region comes from the area of that region. In this setting, area represents the force applied by the distributed load over that part of the beam. After finding the force for each region, the position of each resultant load...

key terms and concepts

Learn how to solve moment of a force problems using free-body diagrams, perpendicular distance, net moment, and rotation direction for high school physics.

Calculating Force Moments in Problem Solving | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Calculating Force Moments in Problem Solving

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