Understanding Differential Equations


Understanding Differential Equations

In physics, work is energy that is transferred from an object to another through the use of pressure or the application of pressure. In its most simple form, it can be described as the result of a change in force and/or displacement. Work done on a machine represents the total energy that is required to move the machine to the location where it needs to be. This can be done in a number of different ways, each of which represents a transfer of work.

Accidentally touching something will decrease the work done because of friction. The work done is equal to the pull of gravity on the object times the distance from the contact point. This means that when you do something like push a chair, you are transferring work from a point A to a point B through the force of gravity. The amount of work done is dependent on the force times the distance. If the force equals the distance, there is a relationship between the two: the work done is directly proportional to the force.

When you drive a car, you are not directly transferring work done when you fill the gas tank, but rather the result of the total amount of gasoline that goes into the tank x the velocity that the gas travels through the engine. You are adding work by driving the car, but the magnitude of this work depends on the speed at which you fill the tank. This is similar to the definition of an integral. An integral can be defined as a relationship that is defined by some quantity, such as the rate at which an object moves through a fixed curve, the slope of that curve, and the distance traveled; in this case, the equation would be: Fraction of constant acceleration times the distance traveled.

A force along a tangent path, such as a tangent circle, will always be zero, because the shape of the circle is such that the zero point will coincide with the origin. So, if the force along the tangent line is zero, then the instantaneous velocity of the system will be zero, also known as the integral of the system. This defines the concept of integration. If a system has a constant acceleration and the average distance is not changing, then the integral term will change only the value of the velocity. Integrals may appear as a curve along some tangent plane, such as a tangent circle, or as a curve on a surface, such as the surface of a ball or a baseball hitting a wall.

If one uses the standard definition of work (overalls), then an integral is a change in the overall value of a unit of measure over time, such as in the definition of kinetic energy. The definition is useful because the derivative of the function is always changing, as it changes with time. Thus, the derivative of an integral, as derived from the Taylor series, is defined as the change in the value of a variable times the integration value. The integral of a function is differentiable, so it can be used to derive newtons in different units.

The torque, as derived from the concept of constructive interference, is a measure of a force applied to a system. It is directly related to the work function, which is a function of the velocity and acceleration of the system under consideration. The force on an object is just the sum of all its moment magnitude components. Momentum is an expression for the changes in the acceleration, while potential energy is defined as the energy a body has due to its motion. Thus, the torque, as defined above, defines torque forces, which are a manifestation of potential energy changes.