Name: work in force and motion
Uploaded: 2023-09-22T11:49:36.000Z
Duration: 1 min 14 s
Channel: JoVE

当作用在物体上的力使其发生位移时，就做了功。功等于沿位移方向的力的标量分量与位移的乘积。
从数学上讲，功可以表示为作用力与物体位移的点积。
功的国际单位是焦耳。当一个一牛顿的力使物体移动一米时，所做的功为一焦耳。
由于功是标量，其大小可为正值、负值或零，具体取决于力相对于位移的方向。

以起重机向上提升重物为例。在此情况下，施加的力与位移矢量方向一致，因此所做的功为正值。

另一个例子是，当对行驶中的汽车施加刹车时，制动力的方向与汽车的运动方向相反。此时，所做的功为负值。

通过无质量不可伸长的绳索在无摩擦滑轮上提升重物时，由于力与位移方向垂直，因此不做功。

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	<li>希伯勒，RC（2016 年）。工程力学:静力学。第十四版，新泽西州:皮尔逊。第 11.1 节，第 581-582 页。</li>
	<li>Meriam， JL、Kraige， LG 和 Bolton， JN （2016）。工程力学:静力学和动力学。第八版，新加坡:John Wiley & Sons。第 7.2 节，第 392-393 页。</li>
	<li>比尔，FP，约翰斯顿，ER，Mazurek，DF，康威尔，PJ 和塞尔夫，BP（2016 年）。工程师的矢量力学。第十一版，纽约:麦格劳-希尔教育。第 10.1A 节，第 575 页。</li>
</ol>

功是机械工程的基本概念，并存在着许多应用场景。了解功的计算方式以及不同类型的功可以帮助我们更好地理解其中的物理过程并使我们能够深入的来了解复杂的问题。 功的定义是力作用在物体上，同时并导致物体沿着力的作用线方向进行移动。它同时也被定义为通过对物体施加力来传递能量从而导致其发生位移的过程。这种能量的转移导致了物体的运动或位置能够发生变化。功可以表示为力与同一方向上位移分量的乘积，或者表示为施加的力与物体所产生位移的点积。SI 系统将一焦耳视为其做功单位，这相当于施加一牛顿的力将会使物体发生一米的位移。 对物体所做功的类型取决于力相对于位移的方向。如果施加的力和位移是彼此平行的，则该力所做的功为正功，如果它们是反向平行的，则所做的功为负功。当施加的力和位移彼此垂直时，所做的功为零。做正功的一个例子是，当起重机通过对负载施加向上的力来提升重物时，它会相对于地面向上移动。例如，当对行驶中的汽车施加制动时，车轮会施加与其运动相反的力，从而对其产生负功。 作用于固定点或于位移垂直的一些力，它们则不会产生功。例如，在支撑物体绕无摩擦的销进行旋转时，无摩擦销将会产生反作用力，在无摩擦表面上进行移动的物体其反作用力是相等的。然而，会产生功的力包括物体的重力和作用在粗糙表面上正在移动的物体所产生的摩擦力。 在某些情况下，多个力所做的功之和为零。例如，通过无摩擦销来进行连接的两个刚体需要大小相等方向相反的力来使其进行运动，因此它们的总功为零。同样，通过可伸展绳索来连接的两个块具有大小相等且方向相反的拉力，从而导致其没有做功。 总体而言，了解哪些力会产生功以及如何计算功，可以为解决复杂的物理问题提供更有效的见解，并使我们能够有效地来管理这些过程以达到期望的效果。

功是机械工程中的一个基本概念，具有广泛的应用。理解功的计算方法以及不同类型的功……

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Virtual Work

虚功

KEY TERMS AND CONCEPTS

关键术语与概念

Work

work in force and motion

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position.

Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In the SI system, the unit of work is the joule. One joule is equal to one newton of force acting over one meter of displacement.

The direction of the force compared with the displacement tells us the type of work done. When the force and displacement are parallel, the work is positive. When they are anti-parallel, the work is negative. When the force and displacement are perpendicular, the work is zero.

A crane lifting a heavy load is an example of positive work. The crane applies an upward force, and the load moves upward. Brakes on a moving car show negative work. The wheels exert a force that opposes motion, so work is done against the car’s movement.

Some forces do no work. This includes forces acting at fixed points or forces perpendicular to displacement. Examples include the reaction at a frictionless pin when a body rotates about it, and the reaction force on a body moving on a frictionless surface. Forces that do work include the weight of a body and friction acting on a body moving on a rough surface.

In some systems, the total work done by multiple forces is zero. Two rigid bodies connected by a frictionless pin need equal and opposite forces for motion, so their combined work is zero. The same idea applies to two blocks connected by an extensible cord, where the tension forces have equal magnitude but opposite signs. Knowing which forces produce work helps explain physical processes and solve mechanical problems.

Work in Force and Motion

work

Work connects force, motion, and energy in mechanics. It happens when a force acts on an object and the object moves along the line of action of that force. Work can also be described as energy transfer caused by applying a force, which leads to a change in the object’s motion or position. Work is calculated as the force multiplied by the part of the displacement in the same direction as the force. It can also be written as the dot product of the applied force and the object’s displacement. In...

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Stable Equilibrium Through Potential Energy

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Spring-Mass Motion and Energy Stability

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Stability of equilibrium in physics and engineering can be studied by using a system’s potential energy. An equilibrium configuration is a state where the system can remain at rest. Stability describes whether the system tends to return to that state after a small disturbance. Problem solving begins by finding the equilibrium points of the system. This is done by setting the derivative of the potential energy function equal to zero and solving for the independent variable values that satisfy...

key terms and concepts

Learn how work is calculated from force and displacement, why it can be positive, negative, or zero, and see real examples from cranes and brakes.

Work in Force and Motion | 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

Work in Force and Motion

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