December 25, 2024

Work is an essential part of the physical world – think about horses pulling a plow through a field, fathers pushing grocery carts down aisles, freshman lifting a backpack full of books above her head, weightlifter launching the shot-put – but it also has its place in the mental and organizational realms. For instance, it can be hard to produce quality work when you’re constantly checking your phone and answering emails, even if the task is exciting or interesting. That’s because work requires a deep level of focus and engagement that is not easily achieved with constant distractions.

Fortunately, there are ways to overcome the distractions and get back to doing great work. One of the best is to embrace “deep work” which involves putting down your phone, eliminating interruptions and dedicating time and space for focused, productive, high-quality work. This is especially important for projects that require you to think deeply and creatively.

The scientific definition of work is quite simple – whenever a force causes a displacement, energy is transferred from the object to the force. The unit for measuring work is the joule (J). For example, if a force of 10 newtons (F) is applied over a distance of 2 metres (s), the amount of work done on the object is equal to F * s = (10 N) * (2 m) = 20 J.

Another way to understand work is by considering it as a vector quantity. Since the displacement and the direction of the force are related, the magnitude of the work done can be inverted by multiplying both the force and the displacement by the cosine of the angle between them. This means that the more the distance of the displacement is away from the direction of the force, the less the amount of work is done. Conversely, if the displacement is parallel to the direction of the force, the amount of work is equal to the magnitude of the force.

In addition, if the direction of the force is perpendicular to the displacement, the work done is zero. For instance, the centripetal force exerted by a pully on a ball moving in a circular motion exerts no work on the ball.

Finally, the work done on a point that moves along a curve C is given by the integral W = C F d x mathbf F cdot mathbf v dt, where the small amount of work dW happens over each instant dt of the path C. This makes the integration path dependent, rather than point independent. For example, the gravitational force of an object that is displaced upwards or downwards by a vertical distance y2 – y1 does no work in either direction. The work is purely vertical. This is known as the law of conservation of linear momentum.