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Work and the work-energy principle

AP.PHYS:
INT‑3.E (EU)
,
INT‑3.E.1 (EK)
,
INT‑3.E.1.1 (LO)
,
INT‑3.E.1.4 (LO)
Physicists define work as the amount of energy transferred by a force. Learn about the formula for calculating work, and how this relates to the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy. Created by David SantoPietro.

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  • female robot grace style avatar for user FoxFace
    Why does one need a cos and theta when we can easily get the work by multiplying F and displacement ?
    - thoroughly confused
    (11 votes)
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    • leafers ultimate style avatar for user Arjuna
      Imagine that your F is at and angle starting at the origin and pointing somewhere between the x and y axis and you distance is along the x axis. To calculate the word done we need to take the x component of the our F and multiply it by the distance. And easy way to do this is multiplying the cosine of the angle and the F. And only the x component of our force matter because the y component is going vertical and doesn't do anything to with the x-axis movement. If that doesn't make sense imagine F is the hypotenuse of your triangle. And the x-component is the base and the y-component is the height. Knowing the angle between the x-axis and our hypotenuse (F) and using our handy knowledge of trigonometry, we know we can use the cosine of our angle multiplied by our hypotenuse (F) to find the x-component because of the intrinsic ration in triangles. I hope this helps.
      (23 votes)
  • leaf green style avatar for user yuenhy
    Hi, i'm unclear about why Wnet=0 indicates that an object is maintained at constant. Could someone please kindly help to explain the relationship for this?

    The reason for having this doubt:
    If Wnet=0, doesn't it mean that the object is not moving at all? Since Wnet also = Fnet(d), it could mean that d=0. Hence there is no work done.

    If looking at the application of the work energy theorem whereby acceleration is assumed to be constant & Wnet=1/2(m)(vnet^2) with Wnet=0, it would mean that the net velocity = 0 as the mass of an object will not change. Hence, isn't it that the object will not be moving, instead of moving at a constant velocity?

    Please kindly help out in clarifying my understanding. Thank you.
    (8 votes)
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    • aqualine ultimate style avatar for user milind
      .. the condition is that if the object is moving at a constant speed/velocity then the net work will be zero is TRUE. this is bcoz when u move at a constant velocity then the acceleration is zero bcoz u maintain ur speed instead of increasing or decreasing ur speed . it leads to zero acceleration and NOT constant acceleration. force is mass times acceleration. since u have a zero acceleration your force is going to be zero . and since work is force times displacement ur work will also be zero.

      the possibility raised by u that d = 0 is true and work will also be 0.

      if the acceleration is constant it means that ur velocity keeps increasing by equal amounts in equal intervals of time.... hence it cannot be zero. i hope that clarifies......if u still have any doubt plz ask.
      (22 votes)
  • leaf red style avatar for user Brett Okines
    Hi,
    Just trying to understand Kinetic energy. If a mass travels at a constant velocity in one direction and then moves in the opposite direction at the same velocity will the kinetic energy remain the same?
    (7 votes)
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  • duskpin ultimate style avatar for user Draken
    Gravitational Potential Energy does negative work right?
    So why isn't it taking away energy from an object which goes up to a certain height? As told in the previous lecture, the object possesses Potential energy. I dont understand ... why does it have energy at all?!
    (3 votes)
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    • hopper cool style avatar for user Sam Parker
      To calculate Grav. potential energy we use Ep = -G (m1m2/r).
      In order to have 0 grav. potential energy, the denominator, r, would need to be really massive, so that you were "out of the grav, field." But Newton says that grav, fields extend throughout the universe (even though I am hundreds thousands if not millions of miles away from Pluto its mass and my mass are interacting via our respective grav fields.) So it stands to reason that if you are moving something away from an object, you are moving it towards infinity, so towards 0 grav. potential. But if you let go, it converts the energy you supplied it to kinetic energy, so the conservation of energy says that it must have less energy then it did before you let go. In order for it to have less energy than 0, it must be negative.

      It has energy at all because it is still in the gravitational field of the larger object.
      Hope this helps!
      (5 votes)
  • duskpin ultimate style avatar for user Kaustubh Kuvalekar
    What is the exact meaning of 'NET' Force and 'NET' Work?
    (5 votes)
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  • aqualine ultimate style avatar for user George Balderas
    Where does 1/2 come from?
    (2 votes)
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  • blobby green style avatar for user Lillie Reed
    I don't understand 2 things: 1) What are the conditions for when this formula is valid? 2) How does potential energy relate? What if an object is lifted straight up onto a table and placed there? The energy of the system has changed, even if the starting and ending kinetic energies are the same.

    I'd learned that change in energy = deltaKE + deltaPE + Wdoneonsystem, or if all work is done on the system (none by the system), change in energy = Wdone= deltaKE + deltaPE.
    (4 votes)
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  • aqualine ultimate style avatar for user Shreya
    why is the cosine theta needed in some cases, and not in other cases? I noticed that cosine theta was taken out during the net work formula, and wanted to know why? Thank you!
    (3 votes)
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    • starky tree style avatar for user Austin
      Cosine theta is applied in every case of "work" because it determines whether the system energy is positive, negative, or 0 (neutral). After that the term is used, there is no reason to have it in anymore, because it fulfilled it's one purpose, to tell you the amount of energy put into the system. In conclusion, cosine theta is essential to every "work" problem, but once you determine the direction of the force and displacement, it is just taken out of the equation once you use it because it is not needed anymore for any purpose. The reason why David took it out of the net work formula was because he determined the directions of the displacement and force.
      (2 votes)
  • leaf blue style avatar for user gautam gunjan
    A man performs 120J of work in 6 seconds .calculate power?
    (1 vote)
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  • leaf blue style avatar for user gautam gunjan
    Why do we need theta when we are finding work as by multiplying force and displacement we can easily find it?
    (2 votes)
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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. 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. d is the displacement of the object, how far it moved while the force was exerted on it. 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. 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? We could just find the individual amounts of work done by each particular force and add them up. But there's actually a trick to figuring out the net work done on an object. To keep things simple, let's assume that all the forces already lie along the direction of the displacement. That way we can get rid of the cosine theta term. Since we're talking about the net work done on an object, I'm going to replace F with the net force on that object. Now, we know that the net force is always equal to the mass times the acceleration. So we replace F net with m times a. So we find that the net work is equal to the mass times the acceleration times the displacement. I want to write this equation in terms of the velocities and not the acceleration times the displacement. So I'm going to ask you recall a 1-D kinematics equation that looked like this. The final velocity squared equals the initial velocity squared plus 2 times the acceleration times the displacement. In order to use this kinematic formula, we've got to assume that the acceleration is constant, which means we're assuming that the net force on this object is constant. Even though it seems like we're making a lot of assumptions here, getting rid of the cosine theta and assuming the forces are constant, none of those assumptions are actually required to derive the result we're going to attain. They just make this derivation a lot simpler. So looking at this kinematic formula, we see that it also has acceleration times displacement. So I'm just going to isolate the acceleration times the displacement on one side of the equation and I get that a times d equals v final squared minus v initial squared divided by 2. Since this is what a times d equals, I can replace the a times d in my net work formula. And I find that the net work is equal to the mass times the quantity v final squared minus v initial squared divided by 2. If I multiply the terms in this expression, I get that the net work is equal to 1/2 mass times the final velocity squared minus 1/2 mass times the initial velocity squared. In other words, the net work or total work is equal to the difference between the final and initial values of 1/2 mv squared. This quantity 1/2 m times v squared is what we call the kinetic energy of the object. So you'll often hear that the net work done on an object is equal to the change in the kinetic energy of that object. And this expression is often called the work energy principle, since it relates the net work done on an object to the kinetic energy gained or lost by that object. If the net work done is positive, the kinetic energy is going to increase and the object's going to speed up. If the net work done on an object is negative, the kinetic energy of that object is going to decrease, which means it's going to slow down. And if the net work done on an object is 0, it means the kinetic energy of that object is going to stay the same, which means the object maintains a constant speed.