# Relationship between work and velocity

### Work and energy

Work Done by a Force Acting in the Direction of Motion: N/ 2 kg = 5 m/s2, which , of course, means that the velocity of the object will change by. Work is the measurement of the force on an object that overcomes a resistive force (such as friction or gravity) times the distance the object is moved. If there is . Explanation of the Relationship between Work and Mechanical Energy. When you accelerate an object, you are changing its velocity and.

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.

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?

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.

### newtonian mechanics - The relation between work and time - Physics Stack Exchange

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.

And I apply a force of-- let's say I apply a force of 10 Newtons. And I move that block by applying a force of 10 Newtons.

### Relation between power force and velocity in physics

I move that block, let's say I move it-- I don't know-- 7 meters. So the work that I applied to that block, or the energy that I've transferred to that block, the work is equal to the force, which is 10 Newtons, times the distance, times 7 meters. And that would equal 10 times Newton meters. So Newton meters is one, I guess, way of describing work. And this is also defined as one joule. And I'll do another presentation on all of the things that soon.

But joule is the unit of work and it's also the unit of energy. And they're kind of transferrable. Because if you look at the definitions that Wikipedia gave us, work is energy transferred by a force and energy is the ability to work.

So I'll leave this relatively circular definition alone now.

## Introduction to work and energy

But we'll use this definition, which I think helps us a little bit more to understand the types of work we can do. And then, what kind of energy we actually are transferring to an object when we do that type of work. So let me do some examples. Let's say I have a block. I have a block of mass m. I have a block of mass m and it starts at rest. And then I apply force. Let's say I apply a force, F, for a distance of, I think, you can guess what the distance I'm going to apply it is, for a distance of d.

So I'm pushing on this block with a force of F for a distance of d. And what I want to figure out is-- well, we know what the work is. I mean, by definition, work is equal to this force times this distance that I'm applying the block-- that I'm pushing the block. But what is the velocity going to be of this block over here? It's going to be something somewhat faster.

Because force isn't-- and I'm assuming that this is frictionless on here. So force isn't just moving the block with a constant velocity, force is equal to mass times acceleration. So I'm actually going to be accelerating the block.

So even though it's stationary here, by the time we get to this point over here, that block is going to have some velocity. We don't know what it is because we're using all variables, we're not using numbers.

But let's figure out what it is in terms of v. So if you remember your kinematics equations, and if you don't, you might want to go back. Or if you've never seen the videos, there's a whole set of videos on projectile motion and kinematics. But we figured out that when we're accelerating an object over a distance, that the final velocity-- let me change colors just for variety-- the final velocity squared is equal to the initial velocity squared plus 2 times the acceleration times the distance.