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

Work results when a force acting on an object displaces it. It is equal to the product of the scalar component of force along the displacement direction.
Mathematically, work can be given as the dot product of the applied force and the displacement of the object.
The SI unit of work is the joule. One joule is the work done when a one-newton force displaces an object by one meter.
Since work is a scalar quantity, its magnitude can be positive, negative or zero depending on the direction of the force relative to the displacement.

Consider the example of a crane lifting a load upward. Here, the applied force and displacement vectors are aligned in the same direction, so the work done is positive.

In another example, when brakes are applied to a moving car, the braking force acts in the opposite direction to the car&#39;s motion. Here, the work done is negative.

A frictionless pulley lifting a load through a massless inextensible string does zero work as force and displacement are perpendicular.

work

Work is a fundamental concept of mechanical engineering and has many applications. Understanding how work is calculated and the different types of work can help us better understand physical processes and provide insights into complex problems.
Work is defined as the result of a force acting on an object, causing it to move along the line of action of force. It is also defined as the process of transferring energy through the application of force on an object, resulting in its displacement. This energy transfer is responsible for the object&#39;s change in motion or position. Work can be written as the product of the force and the component of displacement in the same direction, or alternatively written as the dot product of the applied force and displacement of the object. The SI system considers one joule as its unit&#8212;this is equal to performing one newton of force over one meter of displacement.
The type of work done on an object depends upon the direction of the force relative to the displacement. If the applied force and displacement are parallel to each other, the work done is positive and if they are anti-parallel, the work done is negative. When the applied force and displacement are perpendicular to each other, the work done is zero. An example of positive work being done is when a crane lifts a heavy load&#8212;by exerting an upward force on the load, it moves up relative to ground level. Negative work occurs, for example, when brakes are applied to a moving car&#8212;the wheels exert a force opposing its motion, resulting in negative work being done on it.
Some forces, such as those acting on fixed points or perpendicular to displacement, do no work. Examples include the reaction at a frictionless pin when the supported body rotates about it, the reaction force acting on a body which is moving on a frictionless surface, etc. However, forces that do work include the weight of a body and friction force acting on a body moving on a rough surface.
In some cases, the sum of the work done by multiple forces is zero. For example, two rigid bodies connected by a frictionless pin require equal but opposite forces for movement, so their combined work is zero. Similarly, two blocks connected by an extensible cord have tension forces of equal magnitude but opposite signs, resulting in zero work.
Overall, understanding which forces produce work and how to calculate work can provide helpful insights into complex physical problems and allow us to manage these processes effectively for the desired results.

Work

Work is a fundamental concept of mechanical engineering and has many applications. Understanding how work is calculated and the different types of work ...

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Mechanical Engineering

Unit 1

Virtual Work

KEY TERMS AND CONCEPTS

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

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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.

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Work in Force and Motion

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