# What is Work done by a force: Definition and 34 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. ### Work done by a normal force (or rather, work NOT done)

This question states that the normal force of the stairs on the woman does NO work. I do not understand how this can be. I would reason like this: The woman propels herself up the stairs using her legs. Her legs push down against the stairs, and the consequent normal force pushes upwards on her...
2. ### Why does the logic of negative acceleration not always indicate negative work?

Knowing that negative work occurs when the force applied to an object opposes the direction of displacement, and that the direction of acceleration vector should align with the force vector, I assumed the correct answer was that the indication of negative work comes from negative acceleration...
3. ### Work calculation for lifting a Tetrahedron-shaped object from the water

Hi, I'm calculating the work done by regular tetrahedron during taking from the water by crane (USING INTEGRALS). I don't know how bad is that solved so if anyone checks my work and gives me some advice or hints I would be very glad. Everything is written in the PDF file. There were given...
4. ### Finding kinetic energy and initial velocity of a cart over time

Here's my list of variables and things to account for: m=100kg Wnc=5000J Wfriction=-500J -Kinetic energy will be doubled (though I don't know how that plays into it exactly) -I don't think there's any PE because it's on level ground My idea of what the equation might be: Wnc +1/2mv^2initial =...
5. ### B How is 1N enough to move a 0.1kg apple 1 meter high?

Example: How much energy is needed to lift an 0.1 kg apple up 1 meter? To hold a 0.1 kg apple against gravity needs 1 Newton of force: F = mg F = 0.1 kg × 9.8 m/s2 F ≈ 1 N But holding an apple is not work, the apple needs to move! So, raising it using 1 N for 1 m (both in same direction!)...
6. ### Climbing a ladder in an elevator

I have found the apparent weight of the man in the accelerating elevator My question is about what speed I should use in the formula for the power output P = F ⋅ speed My common sense tells me that the speed I should us is the speed v the man is climbing the ladder , because if the...
7. ### 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
8. ### Understanding the Work-Energy Theorem

Are the following definitions correct? Work done as energy transferred The energy transferred when the forces between two objects interact Work done by a force Work done = force x distance moved in the direction of force applied (W=F*Δs) Work done by a gas Work done = pressure x change...
9. ### Definition of work done by torque

I' m trying to derive the work done by a torque from W = ∫ F ⋅ ds and I' ve looked up the internet, it said: W = ∫ F ⋅ ds ( since ds = dθ × r ) ---------------------------------------- ( Line 1 ) it can be written as W = ∫ F ⋅ dθ x r this is a vector triple product , thus can also...
10. ### Problem in understaning potential energy

Homework Statement If we lift a block with constant velocity, by applying a force mg upwards, is the work done zero?Homework EquationsThe Attempt at a Solution The work done must be zero as the resultant force is zero, what I don't understand is how does the block get potential energy if no...
11. ### Work: I am having problem determining the elongation in spring

Homework Statement A spring has been attached to an object which is kept on the ground. The spring is initially in its natural length: 'l' when a force 'F' is applied on it. The force 'F' slowly pulls the object so it does not attain any acceleration. There's a point 'P' on the line which is...
12. ### Intuitive explanation of why work done by tension is 0?

Homework Statement Homework Equations Work Done=Force*Displacement in the direction of the force The Attempt at a Solution I tried to solve the problem this way, I wrote these equations for the two masses, T-mg=ma...(i) Mg-T=Ma...(ii) From (i)&(ii), T=[M(g-a)+m(a+g)]/2 and then I would...
13. ### Problem in calculating work done?

Homework Statement See question number 3 Homework Equations Work Done="integral" F*ds The Attempt at a Solution I tried to solve this question using integration, I have replaced F with "1" and ds with "t^2+2t". So I am stuck in at that step. Please help me differentiate it further or solve...
14. ### Calculation of work done by a variable force

Homework Statement See the explanation of work done by variable forces given in my textbook. For calculation of work done by variable forces the author analyses only a small fraction of displacement "ds". And then he makes **assumption** that the force is acting on the particle at an angle...
15. ### Electric Potential due to a single point charge

Please refer to the image attached. So, my doubt is: While calculating dW in the derivation, we know this work is being done by external force, because only then the unit positive charge can be made to move towards the charge +Q. So dW should be equal to Fext.dx but here in the book it is shown...
16. ### Stationary vertical cylinder with heavy piston

Hi, I'm just starting to learn thermodynamics and I'm completely stuck with a problem: 1. Homework Statement A stationary vertical cylinder, closed at the top, contains a gas whose volume may be changed with the aid of a heavy, frictionless piston of weight w. a) How much work is done by...
17. ### 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.
18. J

### Solving for Work: Tips and Hints | Work Equation Explained

Hi, I am new to this forum and to any forums in general. I am not too sure as to how to solve this problem given the shown statements. I know the equation for work is W=F*d but I am not given any distance. The only thing I can think of is to integrate the Force equation with respect to time...
19. T

### Work done by a cycle on the road

Here's a question, " A bicyclist comes to a skidding stop in 10m. During this process, the force on the bicycle due to the road is 200N along the horizontal and is directed opposite to the motion. What is the work done by the cycle on the road?" From the definition of work done, work is the...
20. ### Explaining the Concepts of Force and Energy

1. The dilemma Work (change in energy) is defined as the exertion of a force over a distance parallel to the force. So if force is exerted, but nothing is moved (presumably with two immovable objects), then no energy is changed. But think about the dilemma with a person lifting 100 pounds...
21. ### In 3rd step of Carnot cycle, work done on the piston is pdV?

Hello. First, look at the figure describing Carnot's cycle. In 1st step (A → B) and 2nd step (B → C), I fully understand that the work done on the pistol (surrounding) by the gas (system) is dW = pdV where dV = Adl since F = pA is the only force on the pistol from the gas (I assumed there...
22. ### Work problem - Rope, pulley and brick (applied integration)

If a brick is pulled across the floor by a rope thruogh a pulley, 1 meter above the ground - and work = W, where W = 10N , (in Newton).Show that the horizontal component of W, which is pulling the brick has the size \frac{10x}{\sqrt{1+x^2}} (*) Use this to calculate the amount of work needed...
23. ### Calculating work done by gravity

Homework Statement A 10kg bucket of water is lifted vertically 3.0m at a constant speed. How much work did gravity do on the bucket during this process? Homework Equations Work=Force*Distance (what thought to use) Wext=Fextdcosθ (what the answer key says to use. The Attempt at a Solution My...
24. ### Calculating Work Done by a Variable Force: Tips and Techniques

Homework Statement A force F acts over the block as show in the figure. F have a constant magnitude, but has a variable direction. The direction of F, at any given instant, always is directed to the point P. Evaluate the work done by the force F through the displacement d between the points R...
25. ### Work calculated for a force not producing displacement?

If a force acting on an object displaces the object, then why do we calculate the work done by all the forces acting on the body (those which did not cause the body to move as well as the force which caused the body to move) instead of the work done only by the force responsible for the...
26. ### 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...
27. ### Can someone help me find the angle between two forces?

Can someone help me relearn finding the angle between two forces when solving for work of each forces (gravity, tension, fF, normal)? I remember that cos(90°-α) = sin(α) but what I don't understand is when the angle in between is "90°-α" or when it's just "α". I tried doing this on my own and...
28. ### Finding the WORK done by a crane in lifting a load

Homework Statement A crane lifts its 500N load to the top of the building from A to B. Distances are shown on the diagram. Calculate how much work is done by the crane Known variables: AB= displacement= 50m AC=horizontal distance=30m BC=vertical distance=40m 2. Homework Equations Work...
29. ### B How to check if force is conservative?

given a force F = f(x) i^ + g(y) j^ + h(z) k^ (x,y,z,are coordinates of body) how can i prove or disprove that the force is conservative ?
30. ### How to Calculate Work on an Object with Varying Position-dependent Force?

Homework Statement An object has several forces acting on it. One of these forces is F=alpha xy ihat, a force in the x-direction whose magnitude depends on the position of the object, with alpha (not zero). Calculate the work done on the object by this force for the following displacements of...
31. ### Work done for stationary object

Say I take a brick and push it and it moves, so work is done and chemical energy in my body is transferred into kinetic energy of the brick, which is then transformed to heat energy due to friction, so I have to keep pushing to transfer more of my chemical energy into kinetic energy of the...
32. ### Work Done by Force in First 4 Secs: 0

1. The position x of a particle moving along x-axis at time t is given by the eqn, t=(√x)+2.,where x is in m and t is in s. Find the work done by force in first 4 sec2. W=F.s=mas I first found out x using the given eqn nd then went blank as there was no force or mass given. But the ans is 0
33. ### Deriving the Force-Position Relationship for a Spring Powered Model Car

Homework Statement In your design of an experimental spring powered model car, you note that the speed of the car (mass Mc) increases as the car travels further. The exact relationship is that v(x) = C|x|, where C is a constant and x is the position of the car with respect to the starting...
34. ### Why work done by a force is a scalar product

Why work done by a force was taken as dot product between force applied and displacement caused?