# Potential energy work relationship definition

### Work and energy The concepts of work and energy are closely tied to the concept of force kinetic energy can be derived from the definition for work and from kinematic relationships. In this case, an object's gravitational potential energy with respect to some. Work of force F acting on a body can be defined in several ways. displacement of muscles' insertions in relation to each other, therefore no work is performed. Let us mention two types of potential energy: gravitational potential energy and. An object may have the capacity for doing work as a result of its position in a gravitational field (gravitational potential energy), an electric field The integral form of this relationship is. which can be taken as a definition of potential energy.

Work is done on an object when an applied force moves it through a distance. In our everyday language, work is related to expenditure of muscular effort, but this is not the case in the language of physics. A person that holds a heavy object does no physical work because the force is not moving the object through a distance.

Work, according to the physics definition, is being accomplished while the heavy object is being lifted but not while the object is stationary. Another example of the absence of work is a mass on the end of a string rotating in a horizontal circle on a frictionless surface.

The centripetal force is directed toward the center of the circle and, therefore, is not moving the object through a distance; that is, the force is not in the direction of motion of the object. However, work was done to set the mass in motion. Work is a scalar. If work is done by a varying force, the above equation cannot be used. The work performed on the object by each force is the area between the curve and the x axis.

The total work done is the total area between the curve and the x axis. For example, in this case, the work done by the three successive forces is shown in Figure 1. Figure 1 Acting force changing with position. Kinetic energy Kinetic energy is the energy of an object in motion.

The expression for kinetic energy can be derived from the definition for work and from kinematic relationships. Consider a force applied parallel to the surface that moves an object with constant acceleration. The right side of the last equation yields the definition for kinetic energy: The above derivation shows that the net work is equal to the change in kinetic energy. Potential energy Potential energy, also referred to as stored energy, is the ability of a system to do work due to its position or internal structure.

Examples are energy stored in a pile driver at the top of its path or energy stored in a coiled spring. Potential energy is measured in units of joules. Power is related to how fast a job is done. Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case since they are identical jobs but the power is different. The equation for power shows the importance of time: Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W.

Combining the equations for power and work can lead to a second equation for power. A few of the problems in this set of problems will utilize this derived equation for power.

Mechanical, Kinetic and Potential Energies There are two forms of mechanical energy - potential energy and kinetic energy. Potential energy is the stored energy of position. In this set of problems, we will be most concerned with the stored energy due to the vertical position of an object within Earth's gravitational field.

Kinetic energy is defined as the energy possessed by an object due to its motion. An object must be moving to possess kinetic energy. The amount of kinetic energy KE possessed by a moving object is dependent upon mass and speed. The total mechanical energy possessed by an object is the sum of its kinetic and potential energies. Work-Energy Connection There is a relationship between work and total mechanical energy. The final amount of total mechanical energy TMEf possessed by the system is equivalent to the initial amount of energy TMEi plus the work done by these non-conservative forces Wnc. The mechanical energy possessed by a system is the sum of the kinetic energy and the potential energy.

Positive work is done on a system when the force doing the work acts in the direction of the motion of the object. The formula to find the work done by a particular force on an object is W equals F d cosine theta. W refers to the work done by the force F.

## Mechanics: Work, Energy and Power

In other words, W is telling you the amount of energy that the force F is giving to the object. F refers to the size of the particular force doing the work. And the theta and cosine theta refers to the angle between the force doing the work and the displacement of the object. You might be wondering what this cosine theta is doing in here. This cosine theta is in this formula because the only part of the force that does work is the component that lies along the direction of the displacement.

The component of the force that lies perpendicular to the direction of motion doesn't actually do any work. We notice a few things about this formula.

### Kinetics • Work, Energy, and Power

The units for work are Newton's times meters, which we called joules. Joules are the same unit that we measure energy in, which makes sense because work is telling you the amount of joules given to or taken away from an object or a system.

If the value of the work done comes out to be positive for a particular force, it means that that force is trying to give the object energy. The work done by a force will be positive if that force or a component of that force points in the same direction as the displacement. And if the value of the work done comes out to be negative, it means that that force is trying to take away energy from the object. The work done by a force will be negative if that force or a component of that force points in the opposite direction as the displacement.

• Work and the work-energy principle
• Work and Energy
• Potential energy