# Relationship between work and kinetic energy

### Work and the work-energy principle (video) | Khan Academy

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. In real life, the kinetic energy of the box is going to be constant if its The relation between work and energy is that the work a force does on an. Kinetic Energy: A force does work on the block. The kinetic energy of the block increases as a result by the amount of work. This relationship is generalized in the.

Gravitational potential energy and conservative forces Video transcript In order to transfer energy to an object, you've got to exert a force on that object. The amount of energy transferred by a force is called the work done by that force. The formula to find the work done by a particular force on an object is W equals F d cosine theta.

### Work and energy

W refers to the work done by the force F. 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. 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. If a force points in a direction that's perpendicular to the displacement, the work done by that force is 0, which means it's neither giving nor taking away energy from that object.

## Work and the work-energy principle

Another way that the work done by a force could be 0 is if the object doesn't move, since the displacement would be 0. So the force you exert by holding a very heavy weight above your head does not do any work on the weight since the weight is not moving. So this formula represents the definition of the work done by a particular force.

But what if we wanted to know the net work or total work done on an object? 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.

### Kinetics • Relation between work and energy

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. 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.

## What is kinetic energy?

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.

Energy often ends up as heat, which is thermal energy kinetic energy, really of atoms and molecules. Kinetic friction, for example, generally turns energy into heat, and although we associate kinetic friction with energy loss, it really is just a way of transforming kinetic energy into thermal energy.