# State the relationship between work and energy

### Work and energy | Physics | Science | Khan Academy

To do joules of work, you must expend joules of energy. conservation of energy and the application of the relationships for work and energy, so it is. I would say that Work is energy transferred during a transformation involving movement. Determine the relationship of work done to the change in energy. Background: Newton's 2nd Law (F=ma) states that an object accelerates when it experiences a.

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.

### Work, Energy and Power

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. Negative work is done when the force doing the work opposes the motion of the object. When a positive value for work is substituted into the work-energy equation above, the final amount of energy will be greater than the initial amount of energy; the system is said to have gained mechanical energy.

When a negative value for work is substituted into the work-energy equation above, the final amount of energy will be less than the initial amount of energy; the system is said to have lost mechanical energy.

There are occasions in which the only forces doing work are conservative forces sometimes referred to as internal forces. Typically, such conservative forces include gravitational forces, elastic or spring forces, electrical forces and magnetic forces. When the only forces doing work are conservative forces, then the Wnc term in the equation above is zero.

In such instances, the system is said to have conserved its mechanical energy. The proper approach to work-energy problem involves carefully reading the problem description and substituting values from it into the work-energy equation listed above. Inferences about certain terms will have to be made based on a conceptual understanding of kinetic and potential energy. For instance, if the object is initially on the ground, then it can be inferred that the PEi is 0 and that term can be canceled from the work-energy equation.

In other instances, the height of the object is the same in the initial state as in the final state, so the PEi and the PEf terms are the same.

As such, they can be mathematically canceled from each side of the equation. In other instances, the speed is constant during the motion, so the KEi and KEf terms are the same and can thus be mathematically canceled from each side of the equation.

If you move the book at constant speed horizontally, you don't do any work on it, despite the fact that you have to exert an upward force to counter-act gravity.

### Work and energy

Kinetic energy An object has kinetic energy if it has mass and if it is moving. It is energy associated with a moving object, in other words.

For an object traveling at a speed v and with a mass m, the kinetic energy is given by: The work-energy principle There is a strong connection between work and energy, in a sense that when there is a net force doing work on an object, the object's kinetic energy will change by an amount equal to the work done: Note that the work in this equation is the work done by the net force, rather than the work done by an individual force.

Gravitational potential energy Let's say you're dropping a ball from a certain height, and you'd like to know how fast it's traveling the instant it hits the ground. You could apply the projectile motion equations, or you could think of the situation in terms of energy actually, one of the projectile motion equations is really an energy equation in disguise.

If you drop an object it falls down, picking up speed along the way. This means there must be a net force on the object, doing work. This force is the force of gravity, with a magnitude equal to mg, the weight of the object. The work done by the force of gravity is the force multiplied by the distance, so if the object drops a distance h, gravity does work on the object equal to the force multiplied by the height lost, which is: An object with potential energy has the potential to do work.

In the case of gravitational potential energy, the object has the potential to do work because of where it is, at a certain height above the ground, or at least above something. Spring potential energy Energy can also be stored in a stretched or compressed spring. An ideal spring is one in which the amount the spring stretches or compresses is proportional to the applied force.

## What is the relationship between work and energy?

This linear relationship between the force and the displacement is known as Hooke's law. For a spring this can be written: The larger k is, the stiffer the spring is and the harder the spring is to stretch. If an object applies a force to a spring, the spring applies an equal and opposite force to the object.

This is a restoring force, because when the spring is stretched, the force exerted by by the spring is opposite to the direction it is stretched. This accounts for the oscillating motion of a mass on a spring. If a mass hanging down from a spring is pulled down and let go, the spring exerts an upward force on the mass, moving it back to the equilibrium position, and then beyond.