# What is the relationship of work and energy

### Work and Energy

Relation. The capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are. 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. The purpose of this activity is to compare the work done on a cart to the change in kinetic energy of the cart. Determine the relationship of work done to the.

The potential energy stored in a spring is given by P. Change in potential energy is equal to work. It states that energy is neither created nor destroyed but can only be transformed from one form to another in an isolated system.

Because the total energy of the system always remains constant, the law of conservation of energy is a useful tool for analyzing a physical situation where energy is changing form.

Imagine a swinging pendulum with negligible frictional forces. At the top of its rise, all the energy is gravitational potential energy due to height above the stationary position. At the bottom of the swing, all the energy has been transformed into kinetic energy of motion. The total energy is the sum of the kinetic and potential energies. It maintains the same value throughout the back and forth motion of a swing see Figure 2. Figure 2 A pendulum obeys the law of conservation of energy.

At point C, the potential energy is dependent upon the height, and the rest of the total energy is kinetic energy. Although total energy is conserved, kinetic energy need not be conserved. A collision between two objects with conservation of kinetic energy is called an elastic collision. Colliding objects interacting with losses of kinetic energy due to frictional losses or deformation of an object are called inelastic collisions. In the macroscopic world, most collisions are inelastic; however, losses of kinetic energy are negligible in the nearly elastic collisions between atomic particles and subatomic particles.

For these cases, the law of conservation of momentum and the conservation of kinetic energy yield useful equations. Solving the equations gives the velocities of the two masses after the interaction: Three special cases are instructive: Pool balls have rotational energy and somewhat inelastic collisions, so their behavior only approximates the example.

In other words, the incoming mass m 1 will bounce back off the second mass with nearly the initial speed, and the hit mass m 2 will move slowly after the collision.

Center of mass The concept of the center of mass CM is useful to analyze the motion of a system of particles. The amount of kinetic energy KE possessed by a moving object is dependent upon mass and speed.

- Work and Energy
- Mechanics: Work, Energy and Power

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.

### Work, Energy and Power

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.

## What is the relationship between work and energy?

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. 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. 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.

This compresses the spring, so the spring exerts a downward force on the mass, stopping it, and then moving it back to the equilibrium and beyond, at which point the cycle repeats. This kind of motion is known as simple harmonic motion, which we'll come back to later in the course.

The potential energy stored in a spring is given by: In a perfect spring, no energy is lost; the energy is simply transferred back and forth between the kinetic energy of the mass on the spring and the potential energy of the spring gravitational PE might be involved, too. Conservation of energy We'll take all of the different kinds of energy we know about, and even all the other ones we don't, and relate them through one of the fundamental laws of the universe.

The law of conservation of energy states that energy can not be created or destroyed, it can merely be changed from one form of energy to another.