Why does friction do negative work

Numerical for finding electricity cost Calculate the work done by heart for each beat. Activity Facebook Whatsapp. CA Maninder Singh is a Chartered Accountant for the past 11 years and a teacher from the past 11 years. He teaches Science, Accounts and English at Teachoo. Teachoo is free. The force of gravity and the normal force acting on the package are perpendicular to the displacement and do no work. Moreover, they are also equal in magnitude and opposite in direction so they cancel in calculating the net force.

The net force arises solely from the horizontal applied force F app and the horizontal friction force f. The effect of the net force F net is to accelerate the package from v 0 to v. The kinetic energy of the package increases, indicating that the net work done on the system is positive. See Example 1.

When a is substituted into the preceding expression for W net , we obtain. This expression is called the work-energy theorem , and it actually applies in general even for forces that vary in direction and magnitude , although we have derived it for the special case of a constant force parallel to the displacement.

This quantity is our first example of a form of energy. Translational kinetic energy is distinct from rotational kinetic energy, which is considered later. Kinetic energy is a form of energy associated with the motion of a particle, single body, or system of objects moving together.

We are aware that it takes energy to get an object, like a car or the package in Figure 3, up to speed, but it may be a bit surprising that kinetic energy is proportional to speed squared. We will now consider a series of examples to illustrate various aspects of work and energy. Suppose a What is its kinetic energy? Note that the unit of kinetic energy is the joule, the same as the unit of work, as mentioned when work was first defined.

It is also interesting that, although this is a fairly massive package, its kinetic energy is not large at this relatively low speed. This fact is consistent with the observation that people can move packages like this without exhausting themselves.

Suppose that you push on the This is a motion in one dimension problem, because the downward force from the weight of the package and the normal force have equal magnitude and opposite direction, so that they cancel in calculating the net force, while the applied force, friction, and the displacement are all horizontal. See Figure 3. As expected, the net work is the net force times distance. Thus the net work is. This value is the net work done on the package.

The person actually does more work than this, because friction opposes the motion. Friction does negative work and removes some of the energy the person expends and converts it to thermal energy. The net work equals the sum of the work done by each individual force.

The forces acting on the package are gravity, the normal force, the force of friction, and the applied force. The normal force and force of gravity are each perpendicular to the displacement, and therefore do no work.

So the amounts of work done by gravity, by the normal force, by the applied force, and by friction are, respectively,. The calculated total work W total as the sum of the work by each force agrees, as expected, with the work W net done by the net force.

The work done by a collection of forces acting on an object can be calculated by either approach. Find the speed of the package in Figure 3 at the end of the push, using work and energy concepts.

Using work and energy, we not only arrive at an answer, we see that the final kinetic energy is the sum of the initial kinetic energy and the net work done on the package.

This means that the work indeed adds to the energy of the package. How far does the package in Figure 3 coast after the push, assuming friction remains constant?

Or how much is actually friction acting against this rider's motion? We could think a little bit about where that friction is coming from. So the force of friction is equal to 60 newtons And of course, this is going to be going against his motion or her motion. And the question asks us, find the speed of the biker at the bottom of the hill. So the biker starts up here, stationary. That's the biker. My very artful rendition of the biker. And we need to figure out the velocity at the bottom.

This to some degree is a potential energy problem. It's definitely a conservation of mechanical energy problem.

So let's figure out what the energy of the system is when the rider starts off. So the rider starts off at the top of this hill. So definitely some potential energy. And is stationary, so there's no kinetic energy. So all of the energy is potential, and what is the potential energy? Well potential energy is equal to mass times the acceleration of gravity times height, right?

Well that's equal to, if the mass is 90, the acceleration of gravity is 9. And then what's the height? Well here we're going to have to break out a little trigonometry. We need to figure out this side of this triangle, if you consider this whole thing a triangle. Let's see. We want to figure out the opposite. We know the hypotenuse and we know this angle here.

So the sine of this angle is equal to opposite over hypotenuse. So, SOH. Sine is opposite over hypotenuse. So we know that the height-- so let me do a little work here-- we know that sine of 5 degrees is equal to the height over Or that the height is equal to sine of 5 degrees. And I calculated the sine of 5 degrees ahead of time.

Let me make sure I still have it. That's cause I didn't have my calculator with me today. But you could do this on your own. So this is equal to , and the sine of 5 degrees is 0.

So when you multiply these out, what do I get? I'm using the calculator on Google actually. You get So this is equal to So the height of the hill is So going back to the potential energy, we have the mass times the acceleration of gravity times the height. Times And this is equal to, and then I can use just my regular calculator since I don't have to figure out trig functions anymore.

So so you can see the whole thing-- times 9. So this is equal to 38, joules or newton meters. And that's a lot of potential energy. So what happens? At the bottom of the hill-- sorry, I have to readjust my chair-- at the bottom of the hill, all of this gets converted to, or maybe I should pose that as a question.

Does all of it get converted to kinetic energy? We have a force of friction here. And friction, you can kind of view friction as something that eats up mechanical energy. These are also called nonconservative forces because when you have these forces at play, all of the force is not conserved. So a way to think about it is, is that the energy, let's just call it total energy.