What is Work-energy theorem: Definition and 95 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:




W
=
F
s
cos


θ



{\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. P

    Misunderstanding Work-energy theorem and center of mass properties

    To do this apparently, you need to use the work-energy theorem. You can calculate work done by gravity easily. However it was said that work done by the reaction forces from the hinge is zero, I don't get why. Reaction Force from the hinge is an external force on the rod, and all external...
  2. P

    Difficulty in deciding when to apply work energy theorem

    This is how I tried to do it. The force required to move B up the incline is $kx$ where x is elongation and k is spring constant. we know that spring force is greater than $mg(sin\theta+\mu cos\theta)$. And we can use work-energy theorem to figure out velocity. $0.5*k*x^2=0.5*mv^2$ where...
  3. Argonaut

    Work-Energy Theorem and Friction

    My final answer is different from the official one in the back of the book, and I can't figure out what I did wrong. This is my attempt: Let block 1 be the vertically moving block and let block 2 be the horizontally moving one. Also, let ##m_1 = 6.00 ~\rm{kg}##, ##m_2 = 8.00 ~\rm{kg}##, ##v_0...
  4. Argonaut

    Understanding Work-Energy Theorem: Solving an Exercise with Different Solutions

    My solution is different from the official solution and I don't understand what I did wrong. Here is my solution: The magnitude of the initial velocity is ##|v_0| = 12.0~\rm{m/s}##, so the vertical component of the initial velocity is ##v_{0-y} = (12.0 \sin{25^{\circ}})~\rm{m/s}##. Then I use...
  5. Philip551

    Solving a Motion Problem with Work-Energy Theorem

    I have been trying to solve the following problem: Point-like object at (0,0) starts moving from rest along the path y = 2x2-4x until point A(3,6). This formula gives the total force applied on the object: F = 10xy i + 15 j. a) Find the work done by F along the path, b) Find the speed of the...
  6. 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...
  7. sachin

    Applying the Work-Energy theorem to a system

    I am trying to solve the given question based on energy conservation,but am stuck with the analysis of the equations. The question says find the velocity of the bigger block when the smaller block initially given a velocity v and sliding on the horizontal part of the bigger block reaches the...
  8. Z

    Possible to use work-energy theorem from a non-inertial frame?

    In learning about translational and rotational motion, I solved a problem involving a wheel rolling down an inclined plane without slipping. There are multiple ways to solve this problem, but I want to focus on solutions using energy. Now to my questions. The reference frame in the posted...
  9. P

    What exactly does the Work-Energy theorem say?

    My research leads to 2 slightly different equations. See equations 1 and 2 attached. Also, for equation 1 should Wext be Wnet ext ?
  10. Soyuz42

    Work Done by Elevator Cable in Sample Problem 7-6

    As stated, part (a) says that the work done by the gravitational force ##\vec{F_g}## is 59 kJ. If ##W_T## is the work done by the elevator cable during the 12 m fall, then using the work-kinetic energy theorem, \begin{align*} K_f -K_i &= W_g + W_T\\ \frac12m({v_f}^2 - {v_i}^2) &= 59000 + W_T\\...
  11. ArtVandolay

    I Relativistic Work-Energy Theorem: Deriving Griffiths' Formula

    In deriving the work-energy theorem, Griffiths does the following: ##\frac{d\mathbf{p}}{dt}\cdot\mathbf{u} = \frac{d}{dt}\bigg(\frac{m\mathbf{u}}{\sqrt{1-u^2/c^2}}\bigg)\cdot\mathbf{u}=\frac{m\mathbf{u}}{(1-u^2/c^2)^{3/2}}\cdot\frac{d\mathbf{u}}{dt}## I may have forgotten something essential...
  12. n3pix

    What does this mean ##U=\int F\times d\vec{r}## in the Work-Energy Theorem?

    Hello, I'm newly discovering the world of the Energy. My question is about the equation ##U=\int \vec{F}\times d\vec{r}=-\int \vec{F}_{s}\times d\vec{r}##. Can you tell me what does this equation means? Thanks!
  13. A

    Is this work-energy theorem for a system correct?

    Homework Statement [/B] A 4 kg mass slides 2 m over a horizontal surface with force of kinetic friction of 2N, initial velocity is 5 m/s. Find it's final velocity. My problem... we've been asked to solve this problem using the Work-Energy theorem, and we've been given it in the form of: W =...
  14. G

    When is Gravitational Potential Energy Considered in the Work-Energy Theorem?

    When using the work-energy theorem (Wnet=ΔE), when do you take gravitational potential energy into account? Change in energy implies all types of energy involved, but in what cases would PEg be a part of it?
  15. vdvdlk

    Work-Energy theorem if the particle´s mass depends on time

    This weekend I was trying to calculate the work-energy theorem, considering a body that can be treated like a particle, and has its mass varying in time. I searched through a lot of sites if such thing existed, and didn´t find anything. Then I found a thread...
  16. donaldparida

    Generalized version of work-energy theorem

    I know that for rigid bodies only the work-energy theorem states that the net work done on the body equals the change in kinetic energy of the body since a rigid body has no internal degrees of freedom and hence no other forms of energy such as potential energy. Is there a most generalized form...
  17. D

    Question About Work-Energy Theorem

    Very simple question. So I am on a homework problem, and I want to make sure that I am using this theorem correctly. My book states that the Work-Kinetic Energy Theorem is: W=ΔK Now the solution to this problem involved multiple forces and thus each force is doing work. So my question is, is...
  18. S

    Doubts on Work-Energy theorem for a system

    While studying energy conservation on Morin I found this explanation about the work-energy theorem for a system. Using Koenig theorem $$\Delta K_\textrm{system}=\Delta K +\Delta K_\textrm{internal}$$ so we have I've got two main question on that: Why are only external forces considered for...
  19. normal_force

    Kinetic energy object vs opposing KE object?

    Homework Statement There is a Ball that weights .150 kg and is moving at 90m/s =607.5 Joules and it is moving to the right, so its coming from the left. on the opposing side is a 35kg cart moving at 4.5m/s = 354.37 Joules The Cart has superior momentum and mass... however, in this scenario some...
  20. D

    Use the work-energy theorem to derive an expression for v^2

    Homework Statement Homework Equations Work energy theorem The Attempt at a Solution .5mv2 - .5mv2 = (kx - μmg)d final velocity is 0 ½mv2 =(kx - μmg)d solve for v2 ((kx - μmg)d2)m When this was wrong I tried integrating Fx but it was still wrong
  21. J

    Work-Energy Theorem problem

    Homework Statement Hi everyone, I have a problem that has me stumped and would appreciate some pointers as to where I am going wrong and maybe point me in the right direction for solving the problem. The problem is in essence to use the "Work-Energy Theorem" to find the co-efficient of kinetic...
  22. D

    Why is the work done and force applied different in the Work-Energy Theorem?

    Assuming you are lifting a block up 1 meter from rest to rest with constant work. You know that the work is -deltaU or 10. However, you also know W=deltaKE which is 0. You finally know that W=Fx=10*F. How do you explain why the numbers are different? Thanks!
  23. F

    Why do I not get the same result when I use change in PE?

    I found the answer to this problem using the change in KE, but when I try to relate the work done on the 12.0-N block in terms of potential energy i don't get the same result. Is the change potential energy not equal to the work done? I would also like to know what situations is the change PE...
  24. S

    Gravitational Work: Ball & Earth Interaction Analysis

    If an object (a ball) begins at rest and falls a distance (h) there is a transformation of gravitational potential energy into kinetic energy (the ball is moving at time-final for my analysis), resulting in a zero net change of total energy for this ball. But, gravity was doing positive work...
  25. H

    How does the velocity of a mass spun around a pencil change?

    Suppose a mass ##m## is attached to the end of a string whose other end is attached to a cylindrical pencil. The mass is then spun around the pencil in a circle (whose centre coincides with the centre of the pencil) such that the string wraps around the outer surface of the pencil, thereby...
  26. Calpalned

    Find speed using the work-energy theorem

    Homework Statement A 96-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 350 N. For the first 15 m the floor is frictionless, and for the next 15 m the coefficient of friction is 0.25. What is the final speed of the crate? Homework Equations Work...
  27. A

    Deriviation for law of conservation of energy

    I'm a bit confused about how the work-energy theorem for a single particle can be extended into the general law of conservation of energy for the macroscopic system, particularly the point where we divide the kinetic energy of the system into macroscopic kinetic energy and internal kinetic...
  28. DiracPool

    Math question related to the work-energy theorem

    There’s a mathematical physics question I have that’s been bugging me lately. I’m not a mathematician so I don’t know if my logic is mathematically “legal” or sound. Part 1 1. Say we restrict ourselves to one dimension and define a spatial coordinate, x. Then we square it, so now we have...
  29. I

    Implications of Work-Energy Theorem

    Wnet = ΔKE By this equation, if I lift a 1 kilogram book at rest from the ground and place it to be at rest on a table 10 meters above the ground, no net work has been done on the book. (Its kinetic energy before and after is zero.) However, its potential energy has changed by mgh or 1kg *...
  30. C

    Work-Energy Theorem Algebraic Representation

    Homework Statement A car of mass m accelerates from speed v1 to speed v2 while going up a slope that makes an angle θ with the horizontal. The coefficient of static friction is μs, and the acceleration due to gravity is g. Find the total work W done on the car by the external forces. Homework...
  31. DiracPool

    What's wrong with my integration for the work-energy theorem?

    I'm having trouble with an integral involved in deriving the work-energy theoremHomework Statement I'm trying to get from ∫mv/√(1-v^2/c^2)dv to -mc^2(1-v^2/c^2).Homework Equations The Attempt at a Solution I start out by putting gamma on top to yield: ∫mv(1-v^2/c^2)^-1/2, then I square...
  32. S

    Why Is Mass Halved in the Work-Energy Theorem Derivation?

    Hello, Someone could explain me why in the derivation below the mass m is divided by 2 in the last step?: ##\int\vec{F}\cdot d\vec{s}=m\int\frac{d\vec{v}}{dt}\cdot\vec{v}dt=\frac{m}{2}\int \frac{d}{dt}(v^{2})dt##
  33. K

    Speed to give box up incline to reach top (work-energy theorem)

    Hi guys, I have come across a problem that I thought I was doing correctly but it seems I am not as my answer seems way too easy and is not the right one either. I don’t need the question worked out for me. I just need someone to give me a nudge in the right direction.Homework Statement “You...
  34. S

    Work-Energy Theorem locomotive Question

    Homework Statement A locomotive exerts a 20 000 Newton force upon a train. It propels four cards, each with a 15 tonne mass. The locomotive's mass is 40 tonnes and friction is considered negligible. Initially at rest, the train accelerates over a distance of one kilometer. a) What is the...
  35. D

    Minimum work and work-energy theorem

    Hi guys, I've got a doubt concerning to the minimum mechanical work and the work-energy theorem. Consider the following Tippens' problem (8.4): A 5-kg hammer is lifted to a height of 3 m. What is the minimum required work? The answer looks very simple and inocent, W = weight times...
  36. skate_nerd

    MHB Problem using integral form of Work-Energy Theorem

    The problem is that the Earth has lost all velocity and begins plummeting toward the sun. I need to find the time it takes for it to hit the sun. Note: Primes indicate "dummy variables" This solution begins with the Work K.E. Theorem...
  37. S

    Deriving The Work-Energy Theorem

    Homework Statement Trying to derive the work-energy theorem, without manipulating differentials.Homework Equations a=\frac{dv}{dt} v=\frac{dx}{dt} W=\int F dx =ΔKE=\frac{1}{2}mvf^{2}-mvi^{2} The Attempt at a Solution F=ma \int F dx=m\inta dx =m\int\frac{dv}{dt}dx <-- I cannot continue...
  38. S

    Finding the Compression of a Spring Using the Work-Energy Theorem

    Homework Statement A 6.0kg box moving at 3.0m/s on a horizontal, frictionless surface runs into a light spring of force constant 75 N/cm. Use the work-energy theorem to find the maximum compression in the spring. Homework Equations W = K2 - K1 W = (1/2)*m*v^2 - (1/2)*m*vo^2 W = -...
  39. M

    Calculate Velocity of 10kg Block on Incline Plane | Work-Energy Theorem

    10kg block is pulled up an incline plane at 30 degree with horizontal in distance 5.0m by force 120N.coefficient of kinetic energy 0.4. help!how do you get the velocity of block? answer: v=3.48ms^-1
  40. Y

    Using the Work-Energy Theorem to Solve a Textbook Sliding Problem with Friction

    Homework Statement A 2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant, k, of 250N/m, compressing the spring a distance of 0.250 m. When released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction μk=0.30. Use the...
  41. A

    Deriving x(t) from work-energy theorem

    In K&K's text on mechanics, after they present the derivation of the work energy theorem: \frac{1}{2}mv^2-\frac{1}{2}mv_0^2=\int_x_0^x F(x) dx It is mentioned that since v=\frac{dx}{dt}, we could solve for \frac{dx}{dt} and integrate again to find x(t) I tried that with v_0=0 just to make...
  42. Vorde

    Work-Energy Theorem with Line Integrals

    Homework Statement The problem is to prove the work-energy theorem: Work is change in kinetic energy.Homework Equations Line integral stuff, basic physics stuff. The Attempt at a Solution I'm given the normal definitions for acceleration, velocity and I'm given Newton's second law. I'm...
  43. L

    Solving the Work-Energy Theorem Error in Block-Table System

    A block (2 kg) is moving with an initial speed of 1 m/s on a horizontal rough table comes to a stop eventually. Applying work-energy theorem to the block-table system, we obtain Change in the kinetic energy of the block + Change in the kinetic energy of the table = Net work done on the...
  44. P

    Work-Energy Theorem HW help

    Help! I am a starter physicist and I need hlep on this question stated thus: Homework Statement A sled is being pulled across a horizontal patch of snow. Friction is negligible. The pulling force points in the same direction as the sled's displacement, which is along the +x axis. As a result...
  45. jaketodd

    Is there a relativistic version of the work-energy theorem?

    The work-energy theorem is stated here on Wikipedia. On the same page it says "regardless of the choice of reference frame, the work energy theorem remains valid and the work done on the object is equal to the change in kinetic energy." I am wondering if there is a relativistic version of...
  46. E

    Proving the Work-Energy Theorem A lot of calculus, anyone?

    Homework Statement A particle moves on a curved path from (x1, y1,z1) to (x2, y2,z2). At the start, the particle has a velocity of v = v1xi+v1yj+v1zk. This curved path can be divided into segments infinitesimally, which are, dl = dxi +dyj +dzk. It is acted on by a net force F = Fxj + Fyi +...
  47. J

    How to use the work-energy theorem to find mu?

    Homework Statement please check this link out to make it simpler to understand... http://www.scribd.com/doc/62694749/MC-Collision1D2 there is a friction block and a spring scale... it gives two measurements (the vertical force and the horizontal force) Fvertical=88.2 N and Fhorizontal=75.8 N...
  48. J

    Work-energy theorem question

    Homework Statement A 34.0 kg crate is initially moving with a velocity that has magnitude 3.70 m/s in a direction 37.0 degrees west of north. How much work must be done on the crate to change its velocity to 6.08 m/s in a direction 63.0 degrees south of east? Homework Equations...
  49. T

    Work-Energy Theorem question with not much detail to work with

    Homework Statement Suppose a hockey puck of mass m is at rest on the ice. A surly Canadian hits the puck and sends it sailing across the ice at velocity v. According to the work-energy theorem, how much work did the player's stick do on the puck?
  50. P

    Work-Energy Theorem: Understanding Vertical Movement

    Hi, i am having a slight confusion with this theorem. I understand that if a car travels horizontally for s m at the uniform acceleration, the Net Work Done = Change in K.E. (by Work-Energy Theorem) The change in K.E. is the amount of joules required to exert the amount of Net Force on the...
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