Force, Work, and Power Equations in Physics

In the field of physics there lies a multitude of equations that once solved can unlock the secrets of the universe. One might think these equations extremely complex and hard to comprehend, but in all reality once broken down these equations are very simple and easy to use. Another amazing aspect of these equations is you can solve for any part of it, no matter what the variables, using simple algebra and trigonometric techniques.

One thing before we continue further, is that you must have some basic understanding in the field of physics. You must understand what mass, velocity, acceleration, and have a simple knowledge of what gravity is. Along with this knowledge it helps to be familiar with SI units such as kilograms, meters per second, and meters per second2. This previous units are known as mass, velocity, and acceleration respectively. Now, let’s move onto the first equation that we will find. This is known as force. Force is a measurement of an objects mass to the magnitude of its acceleration. From the basic force equation both mass and acceleration can be found by simple rearrangement of the equation. Force would appear like so:

Force = (mass) x (acceleration)

or

F = ma

The units that come out of a force equation amount to a (kg)(m)/s2

which in physics is denoted as a Newton (N). This equation helped us discover the acceleration of an object due to gravity alone, which as it so happens is -9.81 m/s2

here on earth’s surface. I won’t go into detail on this subject because velocities and frictions must be calculated which can cause further complications, but any physics text book on the world will agree with me on this one.

From the force equation both mass and acceleration can be found with a simple rearrangement of the variables. Essentially you divide either mass or acceleration across to solve for the unknown you need. For example:

mass = Force / acceleration

or

m = F / a

acceleration = Force / mass

or

a = F / m

These two equations can be further broken down to solve for velocities, displacements, and time intervals if you so choose. Along the same lines, the system of force equations can be plugged into other physics equations to find new measurements and calculations. For instance, force feeds into an equation known as work, which is a measurement of how a force is distributed over a distance. Anytime a force is applied to an object, and the object moves across a plane work is done upon it. Whenever an object’s displacement is zero, then the total work done upon it is zero. One interesting note to make is that an object can have work done upon it, but its net work (total work) can still equal zero because its total displacement was zero.

The work equation produces an interesting set of units. In its most simplified form it’s known as a Joule (J). A joule breaks down to a N*m or a Newton-meter. This can be further broken down into [(kg)(m)/s2 ]*m which is a complicated expression called a kilogram-meter per second2 -meter. Honestly that term is useless to you, but the break down of units is an interesting concept all the same. So just stick to Joules or at the very least a Newton-meter. The work equation can be broken down with the same algebraic concepts as the force equations above. So the work system of equations breaks down as such:

Work = Force x displacement

or

W = (F)(x)

Displacement = Work / Force

or

x = W / F

Force = Work / displacement

or

F = W / x

The outcome of the work equation surmounts to the amount of energy being exerted upon an object. Based upon the law of conservation of energy, the work done upon an object equals all other types of energy in a physical system added together. This is because one of the Laws of Thermodynamics states that all energy in the universe is conserved, and that energy is never destroyed nor created; only transferred. This means that the work equation can be useful in solving for different energies occurring in a physical system you are observing.

The work equation then feeds into yet another system of equations known as power. Power is basically the rate at which work is done. That means once you find the work being done on an object, if you find the time interval you will be able to calculate the total power of a system. Power is measured in watts, which when broken down equals to a N*m/s. Breaking it down any further would be unnecessary and overly complex. Please recognize that a N*m/s is equal to a J/s or Joule per second. This should hint at the power equation’s definition. Energy (or work) over a time interval. The system of equations breaks down as follows:

Power = Work / time

or

P = W / t

Work = Power x time

or

W = (P)(t)

time = Work / Power

or

t = W / P

One might note that watts are used in the measurement of electricity. Well as you advance further in physics you will realize that forces and energies come in many forms, one of those being electrical. Power is a useful equation in many ways, especially when designing simple machines and trying to increase efficiency ever closer to that intangible 100%. I went into the conservation of energy law earlier, but a little more on that node is that you can only get as much energy out of something as you have put into it. If you put 1000 watts of power or 25 Joules or 87 Newtons into a physical system, then it will remain in said system until transferred out or until the universe comes to an end.

With these three base equations and their derived counterparts you can now solve for forces, work, and power of objects in the universe. Not only that, placing further broken down equations into the systems above will allow you to solve for such things as velocities and displacements. Calculations such as these form the building blocks of our universe in which all matter and energies are interrelated. Keep reading, for there’s a crazy world of physics out there to learn!