# What is Work and energy: Definition and 333 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. ### I Work to move a point charge from infinity to the centre of a charge distribution

Electrostatic potential $$\Phi(\vec{r})=k \int \mathrm{d}^{3} r \frac{\rho\left(\vec{r}^{\prime}\right)}{\left|\vec{r}-\vec{r}^{\prime}\right|} (i)$$ with $$k=\frac{1}{4\pi\epsilon_{0}}$$ in SI units. What work is required to move a point charge q from infinity to the center of the through...
2. ### Integral for work done leading to potential energy sign confusion

What is the work done by gravity in moving the particle from a distance of ##\infty## to a distance ##R## from the centre of the Earth (where ##R## > the radius of the Earth)? The answer is obvious, since the displacement and the force of gravity are in the same direction. Therefore, gravity...
3. ### To find work done by a variable force

Guys, please look at the following question I am aware of how to take a dot product of 2 vectors whose i,j,k components are given. My issue is with both integrals. I feel it should be '-dx ' rather than dx because x is decreasing , same as in '-dy'.and I'm taught that if x is decreasing then...
4. ### Bow string problem sign query

The question is easy. I merely have a query: When the bow string is released, the potential energy stored in it ##U = \frac {kx^2} {2}## is all transformed to kinetic energy ##K = \frac {mv^2} {2}##, so we have:$$v = \sqrt {\frac {k} {m}}x$$ I now need to eliminate ##k##, so I can use ##k =...
5. ### Work done for round trip when force is function of velocity

I'd have no problem with this sort of problem if the force were a function of position. But here, I'm not sure where to go. Perhaps I'd start with an expression for the work done over an arbitrary distance if the force is given by ##g(v)##:$$W = \int_a^b g(v) \, dx$$ Not sure what to do next...
6. ### I How come you have to use work energy to find v0 of spring?

If you use work energy, you can get 0.5*k*x^2 = 0.5*m*v^2 to get the velocity if you pulled the spring a distance x. How come you cannot do kx*(delta t) = m*v to get the initial velocity and what would be the delta t value?
7. ### B What is meant by "upper limit of work done on Earth"?

I think that the work is meant to be work done for instance in power stations. Or is it similar to work I do on a body when I lift it for example? But how can we then do that work on our Earth? I just need to understand the task, otherwise I want to solve it myself. The problem involves...
8. ### 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...
9. ### 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...
10. ### When is power constant in this scenario?

Power P = F x v,where F is force and v is velocity, if power remains constant then i think force can not remain constant as it will change the velocity v, but the solution I found is, F = ma, v = at, so, P = F x v = ma x at = ma2 t, after that calculus comes to show that displacement is...
11. ### The Work of Friction: Explained in .32m

The answer is .32m. I set the elastic potential energy as equal to the work, but at first I put the force in the work equation as (F elastic - F kinetic friction) times distance and rearranged. 1/2kx^2 = (kx-Ff) d (0.5) (22) (0.035)^2 = (22 x 0.035-0.042) d 0.013475= 0.728 d 0.013475/0.728 = d...
12. ### Work and Energy for a mass sliding down a curved ramp (why does the ramp move?)

What force causes the surface to move to the left? Can I say that it's due to the force component of the weight along the vertical force of the surface?
13. ### A Calculate work done by a time-dependent pressure to a spherical hole

Hello, Suppose I have a spherical hole in a elastic infinite space. I apply a time-dependent pressure to the inner surface of the spherical hole. I know p = f(t). If I only consider this as an elastic problem, no failure happened, how can I calculate the work done by p during the time from 0...
14. ### B Which Energy Law is the Key to Understanding Work and Conservation?

Hi, everyone! There are a lot of work energy conservation laws and I get confused which one of them summarizes all of them. Which one I should keep with me and rest should be easy to derive on spot ? 1. ##\Delta E_{mec}=0## 2. ##\Delta E_{mec}=W_{ext}## 3.##\Delta E_{mec} + \Delta...
15. ### I Principle of Physics: Derivation of -dU/dx=F

Hi, Everyone! This is the page(first image) from Principle of physics by resnik. I want to ask the definition of work(##W=F(x) \Delta x##) by variable force here is somewhat different from the usual integral version. I don't understand how is this valid definition? Secondly, how did they reach...
16. ### Work and energy of electromagnetic wave with intensity I

a) ##\rho = \frac{I}{c} = \frac{F}{A}## for a perfect absorber ##F = ma## where ##a = \frac{c}{t}## ##\frac{I}{c} = \frac{mc}{tA}## ##I = \frac{I^2 tA}{mc^2} = \frac{P}{A}## ##P = \frac{I^2 tA^2}{mc^2} = \frac{W}{t}## ##W = \frac{I^2 t^2A^2}{mc^2}## I am unsure what A is. I think it should be...
17. ### 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 =...
18. ### B What is the need for the concepts of Work and Energy (KE)?

What is the need to introduce the concept of work and energy when the motion can be completely understood by the concept of force and acceleration and momentum and velocity and displacement, etc? Why do we need to understand the same thing once again in terms of Work and energy? Also the kinetic...
19. ### B About verification on Kinetic energy and work

1. From resnik, Halliday “Kinetic energy K is energy associated with the state of motion of an object. The faster the object moves , the greater is the kinetic energy” If I am right this means that greater the kinetic energy, greater is its speed. 2. Force transfers energy to the body due to...
20. ### Work and kinetic energy comprehension question

Hello, I’ll start by saying I have the answers and the steps to the solutions, but there’s a comprehension disconnect somewhere that I’m trying to figure out. There are two parts to my question but the second one may not apply depending on the answer to the first. I wasn’t sure from the forum...
21. ### I Work Done/Energy Transferred in One Dimensional Collision

I spend a lot of time thinking about collision problems because for me they are both extremely interesting and often very difficult to grasp when one thinks about them beyond the basics we are taught in introductory or even intermediate university courses. Suppose there is a perfectly elastic...
22. ### Does work = neg or pos change in potential energy?

u = (9*10^9)(1.61*10^-19)^2 * (1/[3*10^-15 ]- 1/[2*10^-10]) u = 7.68*10^-14 J but here the question. I have been taught that W= -U so shouldn't the answer be negative?? When i look up at the solution all other sources say that the W = U and therefore the answer is in postive.

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24. ### B Work and energy: conceptual doubt

Suppose I am sliding a block very slowly on a rough surface. If the block has traveled ##d## distance then work done by me is ##W_1=\mu mg d## and that by friction is ##W_2=-\mu mg d##. Now the energy transferred from me to block is ##\mu mgd## and that taken by friction from block is ##\mu mgd...
25. ### The work that is necessary to pull a hanging chain

This is the solution from my textbook, and I have some questions about the method The mass of hanging chain : $$m_h =\frac m 5$$ the center of mass of the hanging chain : $$h_1 = - \frac{1} {2} \cdot \frac L 5 = - \frac L {10}$$ (the minus sign here means that it is under the table surface)...
26. ### 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...

28. ### 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\\...
29. ### Why is PV work in thermodynamics so difficult to understand?

i can't manage to grasp the concept of PV work in thermodynamics, for example we all know that W= integral(F*dx) like here but this says that, at the end, W doesn't really depend on the gas temperature or reversible process crap at the end W is simply a constant, atmospheric pressure is...
30. ### Find the velocity and acceleration of a pulley in a mass-spring system

This looks like a classical setup but I can't find a solution. We can calculate the energy of the system by looking at the work done by the gravity and the spring. But how do we divide the energy between the kinetic energy of the pulley and the rotation of the pulley?
31. ### Conservative forces vs friction

Hello I've written that homework statement as an example to illustrate my doubt: How can I tell if a force is conservative or not? I've read that, if the curl of the force is 0, it's conservative. But what about the friction force (##f=\mu N##)? Its curl is also zero, but it's not conservative...
32. ### Work & energy VS conservation of angular momentum

Summary:: Would energy method give us a different answer from conservation of angular momentum? Hello, I do not know how to type equations here. So, I typed my question in Word and attached it here. Please see photos. Note: This question is not a homework. I did not find it in textbooks or...
33. ### How Does Joule Thomson Expansion Affect Gas Temperature?

Wikipedia says, Unlike a free expansion , in Joule Thomson expansion work is done causing the change in internal energy. Whether the internal energy increases or decreases is determined by whether work is done on or by the fluid; that is determined by the initial and final states of the...
34. ### Variable friction on an inclined plane and maximum velocity

This problem was from the chapter on Work and Energy so, I thought of using the principle of conservation of mechanical energy. Clearly, the potential energy of the block decreases by mgh (assuming the block has mass m). This energy should have been converted to kinetic energy, but it clearly...
35. ### Maximum height a block reaches after separating from a curved moving ramp

Diagram attached at the endI personally think there's something wrong with this question, and I'd like if someone can tell me whether it's the question that is wrong or my approach. If I attempt the solution thinking that M should be stationary, the solution is simple. 0 - 1/2 mv^2 = -mgh...

37. ### Work is not done by static friction when accelerating a car

A recent thread posed the question whether work is done by static friction in the case of an accelerating car. Before I had a chance to reply, the thread was closed on the grounds that the subject was "beaten to death". Undaunted, I am determined to deliver the coup de grâce here with a simple...
38. ### Velocity of an object on an inclined plane

I used work energy theorem between initial top point and point x along the incline(downwards) i got the expression of v then diffrentiated it to get a maxima but it gives me a wrong ans which is 10/6 but the actual ans is 10/3 please tell me what i did wrong
39. ### Projectile Motion : Work and Energy

The problem is based on a projectile-spring launcher. A ball is loaded into a tube that pushes back a spring and is then launched. The ball was launched straight horizontally not at an angle. I'm trying to find the work done on the ball by the spring. The info I have: Displacement of spring =...
40. ### Calculate the average force used to drag a box up a ramp

I first wrote down that 55% = Eout/Ein I also know that W = (Facos20)(4) and I substitute it into the first equation 55% = Eout/[(Facos20)(4)] But I'm missing two variables here. Did i forget something or is the question missing some information?
41. ### Why does voltage = energy/charge?

When you say ##i = \frac{dq}{dt}## it makes sense since current is the flow of charge over time. But why was voltage defined as ##v = \frac{dw}{dq}## ? What made physicians define it in this way? Is there a mathematical way that can lead to this definition or did they define voltage just on the...
42. ### A Motorcyclist crossing a stretch of land

TA = Ec 0,7*m*g*d = (m*v² /2) 1,4*g*d = (400/12,96) 14*d = (400/12,96) d = 2,2 m No
43. ### Work and energy of an object on a ice slope

Homework Statement: A perfect hemisphere of frictionless ice has radius R=7 meters. Sitting on the top of the ice, motionless, is a box of mass m=7 kg. The box starts to slide to the right, down the sloping surface of the ice. After it has moved by an angle 11 degrees from the top, how much...
44. ### Work of a object moving across surfaces with different friction

Homework Statement: Hetsut is the foreman of a construction project in ancient Egypt. He needs to move a giant block of stone, of mass 12 metric tons, from the docks to the temple grounds. He can go along the roads by traveling 295 meters east, then 89 meters north. Along the roads, the...
45. ### Work of gravity on an object sliding down a frictionless sphere

Homework Statement: A perfect hemisphere of frictionless ice has radius R=6.5 meters. Sitting on the top of the ice, motionless, is a box of mass m=6 kg. The box starts to slide to the right, down the sloping surface of the ice. After it has moved by an angle 20 degrees from the top, how much...
46. ### Total work of a directional wind on a mailman

Homework Statement: Mike the Mailman takes his oath seriously: "Neither snow, nor rain, nor heat, nor gloom of night stays these courageous couriers from the swift completion of their appointed rounds". Even though a blizzard is raging outside, he goes out to deliver the mail. He makes four...
47. ### Work required to attach the bowstring to the bow?

E final = (1/2)(500)(1.14012)^2 = 324.968 J E initial = (1/2)(500)(0.5)^2 = 62.5 J E final - E initial = 262.468 J
48. ### Classical Mechanics Problem Based On Conservation Of Energy

I have tried using Conservation of Energy but I'm getting incorrect answer.
49. ### Inelastic collision problem: Bullet striking a wood block

Hey everyone I'm struggling on the last part of this assignment. I need to find the total work done by the block and the bullet, when the collision happens. The informations is: mblock=0.3 kg mbullet=0.01 kg vg=700 m/s Height=0.72m The final speed after the collision is vf=22.6 m/s and the...
50. ### Water Tank Refilling via Hydraulic Water Pumping System

Based on my understanding, Top Tank Refilling Advantage: Atmospheric Pressure Disadvantage: High Head (Requires more distance, thus more Work since W = f x d) Bottom Tank Refilling Advantage: Low Head Disadvantage: High Static Pressure (Requires more Force, thus more Work since W = f x d)...