What is Work energy theorem: Definition and 108 Discussions

In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, it is often represented as the product of force and displacement. A force is said to do positive work if (when applied) it has a component in the direction of the displacement of the point of application. A force does negative work if it has a component opposite to the direction of the displacement at the point of application of the force.
For example, when a ball is held above the ground and then dropped, the work done by the gravitational force on the ball as it falls is equal to the weight of the ball (a force) multiplied by the distance to the ground (a displacement). When the force F is constant and the angle between the force and the displacement s is θ, then the work done is given by:



{\displaystyle W=Fs\cos {\theta }}
Work is a scalar quantity, so it has only magnitude and no direction. Work transfers energy from one place to another, or one form to another. The SI unit of work is the joule (J), the same unit as for energy.

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  1. AyushNaman

    I Work-Energy Theorem for Moving Block and Spring System?

    In the chapter of center of mass and linear momentum, there are multiple problems involving two block systems connected by a string, with both blocks given certain initial velocities. The goal is to calculate the maximum elongation or compression in the spring. For example, consider this...
  2. xkcda

    Combined Rotation and Translation of a Rectangular Plate

    I tried to solve it using the work-energy theorem.The work done to make it stand on its one vertex should be equal to the change in its kinetic energy. I am confused what will be the value of radius here? I have seen formula of kinetic energy for rolling of circular objects.Can anyone please...
  3. C

    I The far reaching ramifications of the work-energy theorem

    The work-energy theorem is the connection between expressing mechanics taking place in terms of force-and-acceleration, ##F=ma## and representing mechanics taking place in terms of interconversion of kinetic energy and potential energy. The following statements are for the case that there is a...
  4. C

    I Bernoulli's equation and the work energy theorem

    Hello physics researchers, teachers and enthusiasts. I notice one little thing is confusing me in the derivation of Bernoulli's equation in the article, they write:$$dW = dK + dU$$where dW is the work done to the fluid, dK is the change in kinetic energy of the fluid, and dU is the change in...
  5. rudransh verma

    B Work energy theorem by variable force

    Its Good to be Back! From Resnik, Fundamentals of physics: Consider a particle of mass m, moving along an x-axis and acted on by a net force F(x) that is directed along that axis. The work done on the particle by this force as the particle moves from position ##x_i## to position ##x_f## is given...
  6. JackyCheukKi

    Work and Energy on a Slope - How Does a Block Move Up with Zero Net Work?

    Guys, I have a problem that really needs you guys to help, I know it is a stupid question but please bear with me: Context: You have a block on a slope(has friction) you use a string to pull the block up with constant speed. Problem: So according to the network theorem, the work net is equal...
  7. E

    Is conservation of energy derived from the work energy theorem?

    To my mind, there are two distinct approaches to energy problems that different authors tend to use, and I wondered whether either is more fundamental than the other. The first is variations on the work energy theorem, and the second consists of defining a system boundary and setting the change...
  8. nish95

    About the constraint equations of a pulley

    See the solved example as shown in the image. I don't understand how can we write S(A)=2S(B) since integrating V(A)=2V(B) will give us an extra unknown constant and the work done by friction will depend on it. I found the relation 2S(B) + S(A) = const. (somebody confirm if this is right?) so...
  9. P

    Work-Energy Theorem: Is Lifting a Rigid Body Really 0 Work?

    I read on the Internet that the work done by a (rigid) body = the change in Kinetic energy. What if I lift a rigid body slowly and vertically by 1 meter above the Earth's surface so that the initial velocity = final velocity =0? According to the Work Energy theorem as stated on many sites on...
  10. L

    Total Work versus External Work

    Is there an important difference between total work and external work? My knowledge would be that total work a.k.a. net work on a system would be equal to the change in kinetic energy of that system and equal to the line integral of the net force on the system dotted with the differential...
  11. When is Work done by Force Negative or Positive?

    When is Work done by Force Negative or Positive?

    Is it confusing to find when is Work done by a force negative or positive? It indeed can be. Learn in this chapter how the dot product of force and displacement can give you the value of work done by the force and also if it is negative or positive
  12. T

    Question about the Work-Kinetic Energy Theorem - Pulling a cart

    Homework Statement Question from Fundamentals of Physics (Halliday, Resnick, Walker) This figure below shows a cord attached to a cart that can slide along a frictionless horizontal rail aligned along an x axis. The left end of the cord is pulled over a pulley, of negligible mass and friction...
  13. C

    Not sure how to plug in numbers for Work Energy Theorem

    1. The Problem Stament, all variables and given data a 15 kg crate, initially at rest, slides down a ramp 2.0 m long and inclined at an angle of 20 degrees with the horizontal. if there is a constant force of kinetic friction of 25 N between the crate and ramp, what kinetic energy would the...
  14. Clara Chung

    Question about work energy theorem

    Homework Statement Homework EquationsThe Attempt at a Solution I don't know how to do part 5, I know the point of maximum speed is at an angle of 120 degrees because the work starts to be negative, but how do I find of the maximum speed at that point without using vector integration? (I...
  15. What is Work done by a Variable force #6 - YouTube

    What is Work done by a Variable force #6 - YouTube

    The formula Work done = dot product of Force and displacement. However this assumes a constant force F on a particle. What then is work done by a variable force. Watch this video to understand how integral calculus can help us find the work done when the force acting in a particle is variable.
  16. How to Find the Potential Energy of a Particle # 9 - YouTube

    How to Find the Potential Energy of a Particle # 9 - YouTube

    How can one find the potential energy of a particle. The derivation of PE can be done by the fact that change in PE of a particle is equal to negative of work done by a force on the particle. This combined with Kinetic energy work theorem gives us an equation on conservation of mechanical energy.
  17. B

    Non-conservative work energy theorem and potential energy

    Here is problem I quickly made up: Suppose there is a ramp with a height of 6 meters and length of 12 meters. A block of 5 kg is pushed up to the top of the ramp with a constant velocity. The force of friction is 15 N. Here's the confusion: By using the non-conservative force work energy...
  18. B

    Question about work energy theorem

    Hello, I am confused about the work energy theorem. If someone goes up the stairs at a constant velocity, is work being done on the person? After all, Wnet = change in kinetic energy, and that change is zero. This is the original problem that I am trying to solve, from David Morin's Problems...
  19. NoahCygnus

    Does work energy theorem fail while dealing with friction?

    Let's consider a setup consisting of a table with friction, and a block on top of it. Suppose we drag the block across the table with a constant speed. The applied force ##f_{app}## acting through a distance ##d## does a work ##f_{app}d##. The frictional force ##\mu N## is equal to ##f_{app}##...
  20. S

    Work energy theorem and forces at equilibrium -- Conceptual doubt

    A pendulum of mass m and length l is suspended from the ceiling of a trolley which has a constant acceleration a. Find the maximum deflection θ of the pendulum from the vertical. When I used work energy theorem, I got θ = 2 arctan(a/g). But when I took the equilibrium position and equated the...
  21. Pushoam

    Work Energy Theorem: particle, system of particles, rigid body

    Question: A) Derive the work - energy theorem for one particle. B) Check whether it is applicable for a system of particles and a rigid bodyWork - energy theorem for one particle system, total sum of work done by individual forces = work done by total force To show the above equality, let's...
  22. G

    Spring problem using work energy theorem

    Homework Statement A 2.90 kg block on a horizontal floor is attached to a horizontal spring that is initially compressed 0.0360 m . The spring has force constant 860 N/m . The coefficient of kinetic friction between the floor and the block is 0.35 . The block and spring are released from rest...
  23. N

    Find coefficient of kinetic friction of block and ramp.

    Homework Statement A small block is on the point of slipping down a rough ramp inclined at 35 degrees to the horizontal. a) What is the coefficient of static friction between the block and the ramp? Answer μ_s = 0.70 b) The ramp is attached to the edge of a 0.8 m high table. After the block is...
  24. T

    Using Work Energy Theorem to Find Necessary Velocity

    1. The problem statement, all variables and given/ You must push a box up an incline plane (the angle being constant : a), to a person waiting to receive it, who is a distance of h(constant) vertically above you. Though the slope is slippery, there is a small amount of friction with kinetic...
  25. V

    Applying work energy theorem to unifrom circular motion

    Homework Statement attempt to derive the equation of centripetal acceleration using work energy theorem Homework Equations work done = Change in kinetic energy The Attempt at a Solution consider diametrically opposed points occurring in uniform circular motion - displacement = 2*R and let...
  26. normal_force

    KE1 vs KE2, mechanical energy change

    Homework Statement If two objects of unequal mass and unequal Kinetic energy hit each other, they lose some energy to other forms but keep enough to do Work on each other. A good example is a car and wind, a man and ball could also apply, a ball with KE could stop a running man if KE does work...
  27. hackhard

    Why were momemtum, kinetic energy and work introduced?

    why were quantities like momentum, force , potential energy, kinetic energy,work ,etc needed to be introduced in physics? and why were they defined the way they are defined?. would it not be possible to explain nature without defining these quantities or by using alternate physical quantities ?
  28. normal_force

    Impulse of force correct here?

    Im sure Imma mess this up, probably because I am really tired...but I have a bullet that weights .015kg's and is moving at 285m/s, so 609.18J's as with KE. I hit a 70kg block, penetrates .3048 meters thus exerting 1998.62N's of force, which is a lot of force. .3048/285m/s so 0.00106 seconds...
  29. SDewan

    Work Energy Theorem in Spring Block System

    Just got confused that while applying the Work - Energy Theorem in a vertical Spring-Block system performing SHM (considering no other external forces other than gravity), when I apply the theorem from equilibrium position, do I consider the work done by gravity?
  30. S

    Work Done by Spring on a Body Sliding down a rod

    1. The Question Unable to find the work done by spring on the object sliding down the rod as shown below: Homework Equations Work Done by Spring Force : -1/2 * KΔx2 --(1) where k = Spring Constant Δx = Change in Spring Length[/B] 3. Where the problem occurred While seeing the solution...
  31. B

    Applying Conservation of Momentum along the Y axis

    Homework Statement A block of mass ##m## slides down a wedge of mass ##M## and inclination ##\theta## whose surfaces are all frictionless. Find the velocity of the block when it just reaches the bottom of the wedge. Homework EquationsThe Attempt at a Solution I was told that to solve this...
  32. P

    Speed with work energy theorem

    1. Homework Statement The Attempt at a Solution I was wondering if I did something wrong for the 50m. I did the same process of finding the area under the line. I'm assuming it's possible to get the same speed since the net work is the same.[/B]
  33. B

    Problem with making the correct FBD

    Homework Statement Consider a wedge of mass ##m## whose upper surface is a quarter circle and is smooth. The lower part is rough. A small block of same mass is kept at the topmost position and the initial position is shown in figure. The block slides down the wedge. Find the minimum value of...
  34. B

    Maximum extension of a spring on an inclined plane

    Homework Statement A block of mass ##M = 1 kg## is placed of a fixed rough incline of inclination ##\theta=sin^{-1} \frac{7}{10}## and coefficient of friction ##\mu=\frac{1}{\sqrt{51}}##. It is connected to a spring of spring constant 100 N/m. Initially the spring is in natural state with...
  35. B

    Understanding why change in Kinetic Energy is 0

    Homework Statement Find the minimum force ##\displaystyle F## required to move ##\displaystyle M_2##.Details and Assumptions: ##\displaystyle M_1 = 3Kg## ##\displaystyle M_2 = 5Kg## ##\displaystyle \mu_1 = 0.4## ##\displaystyle \mu_2 = 0.6## ##\displaystyle g = 9.8m/s^2## Homework...
  36. B

    Rope hanging from a table, find time taken to fall off table

    Homework Statement A rope of uniform mass per unit length ##\lambda## and length ##L## lies curled on a table, with a short length ##\delta l## of it hanging through a hole in the table. At time zero, the rope begins to slide through the hole. At what time ##t_c## (in seconds) does the end of...
  37. B

    2 sphere system, Conservation of Energy and Momentum

    Homework Statement [/B] A sphere of radius $1m$ and mass $25 Kg$ is put on another sphere of radius $5 m$ and $7 Kg$ which is placed on a smooth ground. Now the upper sphere is pushed very slightly from it's equilibrium position and it begins to fall. Now when the line joining the centre of...
  38. Titan97

    Work energy theorem problem

    Homework Statement A uniform chain of mass m and length l overhangs on a smooth table with two third part lying on the table. Find the kinetic energy of the chain after it slips off the table. Homework Equations F=ma Total work done by all forces = change in kinetic energy The Attempt at a...
  39. M

    Understanding the Work Energy Theorem for a Spring

    Hi, I looked around for hours but it seems like I'm the only one who finds it confusing. I understand the concept of potential energy and work, but have a problem with the equations. Here is what I don't understand: The work energy theorem states that K2-K1=W. W = ∫Fdx from evaluated between...
  40. E

    Question about work, energy and the work energy theorem.

    Homework Statement So a mass m is placed on a ramp at a height given by h_1. This portion of the trip is frictionless. Then, at the bottom of the ramp the mass encounters a rough patch of levelled ground with a µk given my µ. This strip has a length of size "d" meters. After traveling across...
  41. N

    Bernoulli's principle and work energy theorem

    for a stream line flow of ideal liquid (non-viscous) imcompressible the sum of pressure energy per unit volume kinetic energy per unit volume , potential energy per unit volume remains constant mathematically P+1/2roV2+ROGH=constant consider a fluid flowing in a pipe of various crossections we...
  42. S

    Calculating Work and Kinetic Energy in a Cart Experiment

    Mentor's Note: This post and another have been merged at the member's request in order to attach their results. 1. Homework Statement See the attached picture for the lab setup. It is all about releasing a cart of 1.212 kg attached with a string and hanging masses. I recorded the Initial and...
  43. R

    I'm confused about the work energy theorem

    The reason why the work energy theorem " ΣW = Δ KE " only includes kinetic and not potential energy, is because gravity undoes the potential energy ? What I mean by "undoes" here is, If you were to, for e.g., lift an apple up a vertical distance, but also accelerate it while lifting it. Then...
  44. H

    Determine the speed of the rock as it leaves the spring.

    Here is the question: A spring is compressed 20cm. When it is released, it exerts an average force of 57.2 N on a 7.3 kg rock, shooting it across a frictionless floor. Determine the speed of the rock as it leaves the spring. Homework Equations W=change in energy Work energy theorem W=Fd The...
  45. G

    Modern Physics - Work Energy Theorem

    Homework Statement The work-energy theorem relates the change in kinetic energy of a particle to the work done on it by an external force: \triangle K = W = \int F\, dx . Writing Newton's second law as F = \frac{dp}{dt} , show that W = \int v\, dp and integrate by parts using the...
  46. BrainMan

    Non-consecutive forces and work energy theorem

    Homework Statement A dockworker allows a 350-N crate to slide down an incline that is 8 m in length to the deck of a ship 5 m below the dock level. The rough incline exerts a frictional force of 50 N on the crate. (a) What is the speed of the crate as it reaches the deck (b) What is the...
  47. U

    When Does the Kinetic Work Energy Theorem Not Apply?

    When does the Kinetic Work Energy Theorem not apply to a situation? Or better, is there a general form of the equation where work can equal the change in any energy? What is work besides a force and a distance?
  48. L

    Work Energy Theorem and Kinematics

    Homework Statement A small steel ball of mass .0283kg is placed on the end of a plunger of length .0051m attached to a spring 1.88m above the ground. The spring is pre-compressed .0011m and has a spring constant of 177 N/m. The plunger is then angled on a ramp 45° above the horizontal, and is...
  49. J

    Does the Work-Energy Theorem hold true for objects in rotational motion?

    Consider a solid sphere and a cube of equal mass, both on a frictionless table. Now, you apply a force to both objects at the point of contact between the object and the table. Then the linear accelerations of both objects will be the same (since the same force is applied to the two objects of...
  50. M

    Work Energy Theorem for Variable Mass Systems

    How do we know that the work-energy theorem holds for variable mass systems? Or rather, since I'm sure that we can at least know it to be true experimentally, what is the mathematical basis for the work-energy theorem? I know for fixed mass systems, a rather simple derivation comes from...