# What is Work-energy: Definition and 168 Discussions

In physics, energy is the quantitative property that must be transferred to a body or physical system to perform work on the body, or to heat it. Energy is a conserved quantity; the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement in the International System of Units (SI) of energy is the joule, which is the energy transferred to an object by the work of moving it a distance of one metre against a force of one newton.
Common forms of energy include the kinetic energy of a moving object, the potential energy stored by an object's position in a force field (gravitational, electric or magnetic), the elastic energy stored by stretching solid objects, the chemical energy released when a fuel burns, the radiant energy carried by light, and the thermal energy due to an object's temperature.
Mass and energy are closely related. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will increase the object's total mass just as it increases its total energy. For example, after heating an object, its increase in energy could be measured as a small increase in mass, with a sensitive enough scale.
Living organisms require energy to stay alive, such as the energy humans get from food. Human civilization requires energy to function, which it gets from energy resources such as fossil fuels, nuclear fuel, or renewable energy. The processes of Earth's climate and ecosystem are driven by the radiant energy Earth receives from the Sun and the geothermal energy contained within the earth.

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1. ### 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...
2. ### 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...
3. ### 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...
4. ### 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...
5. ### 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...
6. ### How Do Angular and Linear Velocities Relate in Cyclist Work-Energy Problems?

can I get some tips on how to approach this problem ? I don't get where I should start on this one. thank you
7. ### 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...
8. ### 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 ?
9. ### 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...
10. ### Work-energy principle for a block fired up a vertical track

I know how to solve the problem but have a question related to it. When the block is initially released from the spring the spring, having been pulled back, should give an initial velocity to the block. In that case why is the block's initial velocity zero?
11. ### 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!
12. ### Work-Energy in carrying something down

Options are: a) Sara doesn’t do any work on the heavy box of books. b) Sara does a small amount of negative work on the heavy box of books. c) Sara does a small amount of positive work on the heavy box of books. d) Sara does a large amount of negative work on the heavy box of books. e)...
13. ### What are the key mistakes in approaching this work-energy principle problem?

Homework Statement : A skater with mass 70kg standing on ice throws a stone of mass 5kg with a velocity of 8m/s in the horizontal direction. Find the distance over which the skater will move back if the coeffcient of friction between the skates and the ice is 0.02[/B]Homework EquationsThe...
14. ### 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 =...
15. ### Work-energy v.s. impulse-momentum bar charts

My question unfortunately does not fit in the Homework template, so I hope this is okay. I attached a question below which involves multiple parts using the concepts related to energy, work, impulse, and momentum. Under the "Simplify and Diagram" section (you will notice it is in bold text), I...
16. ### 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?
17. ### 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...
18. ### Work-Energy Conservation Question

Homework Statement A ##10.0kg## block falls ##30.0m## onto a vertical spring whose lower end is fixed to a platform.When the spring reaches its maximum comprassion of ##0.200m##,it is locked in place.The block is then removed and spring apparatus is transported to the Moon,where the...
19. ### Work-Energy for Bead on Rotating Stick

Homework Statement Verify the Work-Energy Theorem W=ΔK for a bead of masd m constrained to lie on a frictionless stick rotating with angular velocity ω in a plane. Homework Equations W =∫ F⋅dr, K =m/2 v^2 [/B] The Attempt at a Solution Adopting polar coordinates the velocity is v = r' +r*Θ'...
20. ### Solving a Midterm Physics Problem: Masses A & B with Springs

Homework Statement Masses A and B, each having a mass of 32.2 slugs, are constrained to move in frictionless slots. They are connected by a rigid, massless rod of length L = 2 ft. Mass B is connected to two massless linear springs, each having a spring constant k = 60 lbF / ft. The springs are...
21. ### 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...
22. ### Is My Professor Wrong? Understanding the Work-Energy Principle

See attached file. I believe my professor is incorrect. Work in must equal work out. We can imagine the work done by the mass as being a separate issue. Then, we recognize that the work done by the spring must be the same. Am I right? If not, why?
23. ### Help with the work-energy principle

Homework Statement Homework Equations PE at A = 3mgx WD = Fs KE = 1/2mv^2 The Attempt at a Solution The question I am stuck on is part ii. I worked out from part i that the PE at A is 3mgx, so therefore all this must go towards the KE and the sound, and doing work against friction, etc...
24. ### 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...
25. ### 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...
26. ### Work-energy solution for a hanging weight

Homework Statement Problem - A 120-kg mail bag hangs by a vertical rope. A worker then displaces the bag to a position 2.0 m to the side from the original position, always keeping the rope taut. What horizontal force is necessary to hold the bag in the new position ? Note :- We have to use...
27. ### 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
28. ### Solve Work-Energy Problem for Girl Cliff Diving

Homework Statement A girl is cliff diving. She jumps (assume from rest) from an 80 meter high cliff. a) If her mass is 64 kg, and her body can only withstand a force of 11,000 N without breaking a bone, what is the minimum depth she must go into the water and not get hurt? b) If we assume she...
29. ### Basic hydraulic pump work-energy relationship

I have a very simple question that's been driving me nuts. It's biology context, but probably all the physics equates to normal positive displacement pumps. The pressure in and volume of the left ventricle of the heart can be measured experimentally. (For example...
30. ### 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...
31. ### 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!
32. ### Work-Energy Derivation question: F(x(t)) = F(t) ?

Does this derivation: ...imply: My best guess is that x(t) ≠ t So I would also guess that F(x(t)) ≠ F(t) But then how can this derivation be explained? How can F(x(t)) = m(a(t))? What does that actually mean? How come it's not: F(x(t)) = m(a(x(t))) ? Why/How does the x just cancel...
33. ### Work-Energy principle and spring force

A block lies on a horizontal frictionless surface, and the spring constant is 50 N/m. Initially, the spring is at its relaxed length and the block is station ary at position x = 0 .Then an applied force with a constant magnitude of 3 N pulls the block in the positive direction of the x...
34. ### MHB Mechanics work-energy question

A cyclist starting from rest freewheels for 120m down a slope of 1 in 30. At the bottom of the slope the road becomes horizontal, and the cyclist stops without using his brakes after going a further 40m. If the total mass of the bicycle and rider is 72kg, find the resisting force, assuming it to...
35. ### Can someone check my answer for this work-energy problem?

Homework Statement A mass attached to a string of length L is released from rest from an initial horizontal position (although the diagram implies it is not that high, please ignore that part of the diargram - sorry). From veritcally below where the string is attached at its top, there is a peg...
36. ### 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...
37. ### Can Mathematical Manipulations Validate 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...
38. ### Waterslide and Energy Conservation

Homework Statement Homework Equations Conservation of energy, F=ma The Attempt at a Solution (a) By the conservation of energy, we use points A and C as the initial and final, ## \frac{1}{2} m v^2 - \frac{1}{2} m 2.5^2= (m)(g)(9.76) \Rightarrow v = 14.1 m/s ## (b) Since ## W_{nc} = \Delta...
39. ### 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 *...
40. ### 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...
41. ### 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...
42. ### Work-Energy Principle: Pulley System

Homework Statement (see attatchment) We know masses M and m, and I am trying to describe the downward speed of m in terms of the hight from the ground. There is no friction Homework Equations \sum \text{F} = ma W_{\text{total}} = \Delta K = \int \text{F} \cdot d\text{s} The Attempt at...
43. ### 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##
44. ### Work-energy principle and conservative forces

Hi, all there are equation in the pic but I can't understand them. I know work-energy principle which is W= F * X (work equals force times way) but I think they are special forms. What concepts and topics should I study to understand them?
45. ### Kinematics and Work-Energy problem with skier

Please look at attached picture. Why did my teacher assume that vf does not change upon landing in the last sub-question? This makes no sense to me. Is there such a way that the skier can change direction of vf without changing the magnitude of it? Otherwise, the skier will collide in an...
46. ### Mechanics - Work-Energy Principle Question

Homework Statement a) A car of mass 1050kg moves along a straight horizontal road with its engine working at a constant rate of 25kW. Its speed at a point A on the road is 12ms-1. Assuming that there is no resistance to motion, calculate the time taken for the car to travel from A until it...
47. ### Work-Energy: Determining x- and y-components of wind force

Homework Statement Homework Equations Constant acceleration equations: Δx = v,xi *t + 0.5*(a,x)*t^2 Δy = v,yi *t + 0.5*(a,y)*t^2 K = 0.5*m*v^2 U = mgh W,nonconservative forces = ∫ ∑ F dx Conservation of Energy: K1 + U1 = K2 + U2 ∑F = ma The Attempt at a Solution (Note that in my notation, I...
48. ### Work & Energy: Lifiting Water from a Well

Homework Statement A child lifts a bucket full of water from the bottom of a 5 meter deep well by pulling on a rope. The 10.0 kg bucket accelerates at a rate of 0.250 m/s/s. Determine: a. the work done on the bucket by the child b. the work done on the bucket by gravity c. the total work2...
49. ### Rollercoasters and Work-Energy

Homework Statement A rollercoaster has an initial hill that leads to a circular loop of radius R. (a) Show that the top of the hill must be at least 1/2 R higher than the highest part of the loop. (b) Discuss additional factors that must be considered in the design of an actual rollercoaster...
50. ### Work-Energy involving two forces on a pulley.

Homework Statement Homework Equations The Attempt at a Solution Well, I tried working on this problems a few different ways and kept hitting a dead end. The work in "relevant equations" was my last attempt. I have spent well over an hour on this problem and I am ridiculously...