# What is the relationship between net work and kinetic energy

### What is kinetic energy? (article) | Khan Academy

The relationship between work done on a body and its kinetic energy is very nicely This happens only because in this proofing the work done is equal to net . Learn what kinetic energy means and how it relates to work. Alternatively, one can say that the change in kinetic energy is equal to the net work done on an. The principle of work and kinetic energy (also known as the work-energy theorem ) The relationship between the net force and the acceleration is given by the.

In certain situations there is a relationship between that work and mechanical energy as opposed to heat or radiant energy. When you accelerate an object, you are doing work against inertia, such that the work equals the change in kinetic energy of the object. Change in KE means you have accelerated the object.

When you accelerate an object, you are changing its velocity and thus its KE. By accelerating the object over a period of time, you are moving the object some distance, while changing its veleocity. Thus, you arwe doing work against inertia you are doing work against inertia, such that the work equals the change in kinetic energy of the object.

### Work and energy

When you are doing work against continuous resistive forces, such as gravity or spring tension, work done equals the change in potential energy of the object. Questions you may have include: What is the equation for work? How is work the change in kinetic energy?

If you pick a book off the floor and put it on a table, for example, you're doing positive work on the book, because you supplied an upward force and the book went up. If you pick the book up and place it gently back on the floor again, though, you're doing negative work, because the book is going down but you're exerting an upward force, acting against gravity.

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. 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.

- Relationship between Work and Mechanical Energy

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.

## What is kinetic energy?

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.