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We’re all familiar with the terms “work” and “energy,” and we use them all the time. Work is a general term that encompasses any activity requiring a significant investment of time, energy, or both. When the force applied to a specific area of the body moves towards or away from the force’s direction, it is referred to as work done by a force or work done against the force’s direction in physics. If there is no movement, there is no work done. As a result, two requirements must be met for the work to be completed:
One must use physical force.
The force must cause a movement or displacement.
Categorisation of work into three types
If a force moves an object in the force’s direction, the work done is considered positive. As an illustration, consider the motion of a ball falling toward the ground. Here, the ball is being displaced in the direction of gravity’s pull.
Negative work occurs when the force and displacement are in opposite directions. Displacement in the upward direction is caused by gravity, but the downward motion of the ball counters this force.
The force does not work on the item if the force and displacement directions are parallel.
Force exerted against a wall accomplishes no work since the wall’s displacement is d = 0 when we push firmly against it. Because our muscles rely on our internal energy, we end up exhausted.
Some key points
The direction of motion does not need that a force is applied to an object in the same direction as it moves. W=Fd means that the force acting on an object is multiplied by its displacement to calculate its work.
There’s more to it than just that. It contains a cosine term (assumed) that we don’t account for forces parallel to the movement.
You might wonder, “Why would we do such a thing?” We do this since the two are essentially the same functionality.
If the force is acting in a straight line with respect to a moving object, the cosine term is zero and does not affect the calculation.
A decrease in work done in the direction of motion we’re considering is caused by increasing the force’s angle, whereas an increase in work done in a perpendicular direction is caused by increasing the force’s angle.
There is no effort exerted in the original direction at 90 degrees-angle, and the cosine term is equivalent to 0 because the angle is perpendicular.
Work done by a variable force
The variable force’s work is a little more complicated. As the job progresses, the force might alter both magnitude and direction. Variable force work is the most common in our daily lives.
Because force is proportional to the object’s displacement from its equilibrium position, the force acting at each instant during the spring’s compression and the extension will be different. Thus, the infinitesimally small amounts of work performed during each instant must be counted in order to determine the total amount of work performed.
Such an integral is calculated as follows.
Reviewing and Reinterpreting Hooke’s Principle
When a spring is compressed or stretched, its force is equal to the force required to extend or compress it.
On the other hand, the spring force acts in the opposite direction of the extension.
When the spring is entirely unstretched, the force on the spring is directly proportional to the spring’s displacement.
We are the spring’s elastic potential energy. Hooke’s Law can help evaluate force using this spring force-displacement graph.
So, Fs = -kx
Thus,Ws = Fs vdt
Variable Forces: How to Calculate the Work Performed
To say that a force does work is to say that it affects a body in a way that moves the point of application in the force’s direction of application. As a result, a force is effective if it causes movement.
W = Fx can be calculated when a force of magnitude F is applied to the point that travels in the force’s direction, W = Fx can be calculated.
Calculating the work done with a variable force necessitates integration. As an illustration, consider the work that a spring performs.
Hooke’s law states that the spring force of an elastic coil is inversely proportional to its lengthening or shortening (or expansion or compression) (or compression).
When an object is linked to a spring in the horizontal plane, the spring force acting on it is given by Fs=kx, which is proportional to the object’s x-axis displacement (extension or compression) relative to its equilibrium position on the spring, but it is also perpendicular to x. dt (or, dx = vdt) must be added to the final work done by the variable force to account for all minuscule contributions to the work done in insignificantly short time intervals dt.
Conclusion
Thus, we conclude our brief review on work done by a constant force and variable force in terms of ‘work’ and ‘energy’. We verified the force acting on an object is denoted as W=Fd. We have touched upon the different types of work, such as positive, negative, and zero work. We did a brief analysis on force-displacement where Fs = -kx. Moreover, we have touched upon the Hookes’ Law on a force applied on a spring and reviewed it.
