In physicswork 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.

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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.

Work is a scalar quantity[1] 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 Jthe same unit as for energy. According to Jammer, [2] the term work was introduced in by the French mathematician Gaspard-Gustave Coriolis [3] as "weight lifted through a height", which is based on the use of early steam engines to lift buckets of water out of flooded ore mines.

According to Rene Dugas, French engineer and historian, it is to Solomon of Caux "that we owe the term work in the sense that it is used in mechanics now". The SI unit of work is the joule Jnamed after the 19th-century English physicist James Prescott Joulewhich is defined as the work required to exert a force of one newton through a displacement of one metre.

Non-SI units of work include the newton-metre, ergthe foot-poundthe foot-poundalthe kilowatt hourthe litre-atmosphereand the horsepower-hour. Due to work having the same physical dimension as heatoccasionally measurement units typically reserved for heat or energy content, such as thermBTU and calorieare utilized as a measuring unit. The work W done by a constant force of magnitude F on a point that moves a displacement s in a straight line in the direction of the force is the product.

The work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance. Work is closely related to energy. The work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body.

Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. From Newton's second lawit can be shown that work on a free no fieldsrigid no internal degrees of freedom body, is equal to the change in kinetic energy KE corresponding to the linear velocity and angular velocity of that body.

Work (physics)

The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. Therefore, work on an object that is merely displaced in a conservative force fieldwithout change in velocity or rotation, is equal to minus the change of potential energy PE of the object. These formulas show that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensionsand units, of energy.

Constraint forces determine the object's displacement in the system, limiting it within a range. For example, in the case of a slope plus gravity, the object is stuck to the slope and, when attached to a taut string, it cannot move in an outwards direction to make the string any 'tauter'.

It eliminates all displacements in that direction, that is, the velocity in the direction of the constraint is limited to 0, so that the constraint forces do not perform work on the system. For a mechanical system[7] constraint forces eliminate movement in directions that characterize the constraint. Thus the virtual work done by the forces of constraint is zero, a result which is only true if friction forces are excluded.

physics energy work equation

For example, in a pulley system like the Atwood machinethe internal forces on the rope and at the supporting pulley do no work on the system. Therefore work need only be computed for the gravitational forces acting on the bodies. Another example is the centripetal force exerted inwards by a string on a ball in uniform circular motion sideways constrains the ball to circular motion restricting its movement away from the centre of the circle.

This force does zero work because it is perpendicular to the velocity of the ball. It can change the direction of motion but never change the speed. This scalar product of force and velocity is known as instantaneous power.The concept of work in physics is much more narrowly defined than the common use of the word. Work is done on an object when an applied force moves it through a distance.

In our everyday language, work is related to expenditure of muscular effort, but this is not the case in the language of physics. A person that holds a heavy object does no physical work because the force is not moving the object through a distance. Work, according to the physics definition, is being accomplished while the heavy object is being lifted but not while the object is stationary.

Another example of the absence of work is a mass on the end of a string rotating in a horizontal circle on a frictionless surface. The centripetal force is directed toward the center of the circle and, therefore, is not moving the object through a distance; that is, the force is not in the direction of motion of the object.

However, work was done to set the mass in motion. Work is a scalar. If work is done by a varying force, the above equation cannot be used. The work performed on the object by each force is the area between the curve and the x axis. The total work done is the total area between the curve and the x axis. For example, in this case, the work done by the three successive forces is shown in Figure 1. Acting force changing with position. Kinetic energy.

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Kinetic energy is the energy of an object in motion. The expression for kinetic energy can be derived from the definition for work and from kinematic relationships. Consider a force applied parallel to the surface that moves an object with constant acceleration. The right side of the last equation yields the definition for kinetic energy: K. The above derivation shows that the net work is equal to the change in kinetic energy.

Potential energy. Potential energy, also referred to as stored energy, is the ability of a system to do work due to its position or internal structure. Examples are energy stored in a pile driver at the top of its path or energy stored in a coiled spring.

Potential energy is measured in units of joules. Gravitational potential energy is energy of position.When a fluid flows into a narrower channel, its speed increases.

That means its kinetic energy also increases. Where does that change in kinetic energy come from? The increased kinetic energy comes from the net work done on the fluid to push it into the channel and the work done on the fluid by the gravitational force, if the fluid changes vertical position.

Recall the work-energy theorem. There is a pressure difference when the channel narrows. This pressure difference results in a net force on the fluid: recall that pressure times area equals force.

As a result, the pressure will drop in a rapidly-moving fluidwhether or not the fluid is confined to a tube. There are a number of common examples of pressure dropping in rapidly-moving fluids. Shower curtains have a disagreeable habit of bulging into the shower stall when the shower is on. The high-velocity stream of water and air creates a region of lower pressure inside the shower, and standard atmospheric pressure on the other side.

The pressure difference results in a net force inward pushing the curtain in.

physics energy work equation

You may also have noticed that when passing a truck on the highway, your car tends to veer toward it. The reason is the sameā€”the high velocity of the air between the car and the truck creates a region of lower pressure, and the vehicles are pushed together by greater pressure on the outside.

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See Figure 1. This effect was observed as far back as the mids, when it was found that trains passing in opposite directions tipped precariously toward one another. Figure 1. An overhead view of a car passing a truck on a highway. Air passing between the vehicles flows in a narrower channel and must increase its speed v 2 is greater than v1causing the pressure between them to drop P i is less than P o. Greater pressure on the outside pushes the car and truck together.

If we follow a small volume of fluid along its path, various quantities in the sum may change, but the total remains constant. In fact, each term in the equation has units of energy per unit volume. Making the same substitution into the third term in the equation, we find. Note that pressure P has units of energy per unit volume, too. To understand it better, we will look at a number of specific situations that simplify and illustrate its use and meaning.

In that case, we get.This set of 32 problems targets your ability to use equations related to work and power, to calculate the kinetic, potential and total mechanical energy, and to use the work-energy relationship in order to determine the final speed, stopping distance or final height of an object.

The more difficult problems are color-coded as blue problems. Work results when a force acts upon an object to cause a displacement or a motion or, in some instances, to hinder a motion.

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Three variables are of importance in this definition - force, displacement, and the extent to which the force causes or hinders the displacement. Each of these three variables find their way into the equation for work.

That equation is:. The most complicated part of the work equation and work calculations is the meaning of the angle theta in the above equation. The angle is not just any stated angle in the problem; it is the angle between the F and the d vectors. In solving work problems, one must always be aware of this definition - theta is the angle between the force and the displacement which it causes.

If the force is in the same direction as the displacement, then the angle is 0 degrees. If the force is in the opposite direction as the displacement, then the angle is degrees. If the force is up and the displacement is to the right, then the angle is 90 degrees. This is summarized in the graphic below. Power is defined as the rate at which work is done upon an object. Like all rate quantities, power is a time-based quantity. Power is related to how fast a job is done.

Two identical jobs or tasks can be done at different rates - one slowly or and one rapidly. The work is the same in each case since they are identical jobs but the power is different.

Work, Energy, and Power

The equation for power shows the importance of time:. Special attention should be taken so as not to confuse the unit Watt, abbreviated W, with the quantity work, also abbreviated by the letter W. Combining the equations for power and work can lead to a second equation for power. If this equation is re-written as.

Thus, the equation can be re-written as. A few of the problems in this set of problems will utilize this derived equation for power. Potential energy is the stored energy of position.Samuel J. Summary 7. The work done by a force, acting over a finite path, is the integral of the infinitesimal increments of work done along the path.

The work done against a force is the negative of the work done by the force.

Definition and Mathematics of Work

The work done by a normal or frictional contact force must be determined in each particular case. The work done by the force of gravity, on an object near the surface of Earth, depends only on the weight of the object and the difference in height through which it moved.

The work done by a spring force, acting from an initial position to a final position, depends only on the spring constant and the squares of those positions. The kinetic energy of a system is the sum of the kinetic energies of all the particles in the system. Kinetic energy is relative to a frame of reference, is always positive, and is sometimes given special names for different types of motion.

This is the work-energy theorem. Alternatively, the work done, during a time interval, is the integral of the power supplied over the time interval.

Contributors and Attributions Samuel J. Work done by a force over an infinitesimal displacement. Work done by a force acting along a path from A to B. Work done by a constant force of kinetic friction. Work done going from A to B by one-dimensional spring force.Suppose that, a force is applied an object and object moves in the direction of applied force then we said work has done.

Let me explain in other words. There must be a force applied to an object and object must move in the direction of the applied force. If the motion is not in the direction of force or force is applied to an object but there is no motion then we cannot talk about work.

Now we formulize what we said above. Since force is a vector quantity both having magnitude and direction work is also a vector quantity and has same direction with applied force. We will symbolize force as F, and distance as d in formulas and exercises. If there is an angle between force and direction of motion, then we state our formula as given below.

In this case force and distance are in the same direction and angle between them is zero. Thus, cos0 is equal to 1. If the force and distance are in opposite directions then angle between them becomes degree and cos is equal to The last case shows the third situation in which force is applied perpendicularly to the distance.

Cos90 degree is zero thus, work has done is also zero. From our formula we found it kg. In other words. Look at the given examples below, we will try to clarify work with examples. Example 25 N force is applied to a box and box moves 10m. Find the work done by the force. Since the box moves in X direction, we should find the X and Y components of the applied force. Y component of the force does not responsible for the work.

Motion of the box is in X direction. So, we use the X component of the applied force. I did not mention it in the solution. If it was a different value than 1 I must write it also.

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Example Look at the given picture below. There is an apple having a force applied perpendicularly on it. However, it moves 5m in X direction. Calculate the work done by the force. Example If the box is touching to the wall and a force is applied finds the work done by the force.

Box is touching to the wall and force cannot move it. Because there is no distance we cannot talk about the work. As you can see o ur formula. If one of the variables is zero than work has done becomes zero.

Work Power Energy Exams and Solutions. Work with Examples WORK Suppose that, a force is applied an object and object moves in the direction of applied force then we said work has done. If there is an angle between force and direction of motion, then we state our formula as given below; In this case force and distance are in the same direction and angle between them is zero.

Distance If one of the variables is zero than work has done becomes zero.Power is the rate at which work is done. Mathematically, it is computed using the following equation. The standard metric unit of power is the Watt.

physics energy work equation

As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine.

One horsepower is equivalent to approximately Watts. Most machines are designed and built to do work on objects. All machines are typically described by a power rating.

The power rating indicates the rate at which that machine can do work upon other objects. A car engine is an example of a machine that is given a power rating. The power rating relates to how rapidly the car can accelerate the car.

If this were the case, then a car with four times the horsepower could do the same amount of work in one-fourth the time.

The point is that for the same amount of work, power and time are inversely proportional. The power equation suggests that a more powerful engine can do the same amount of work in less time.

A person is also a machine that has a power rating. Some people are more power-full than others. That is, some people are capable of doing the same amount of work in less time or more work in the same amount of time. A common physics lab involves quickly climbing a flight of stairs and using mass, height and time information to determine a student's personal power. Despite the diagonal motion along the staircase, it is often assumed that the horizontal motion is constant and all the force from the steps is used to elevate the student upward at a constant speed.

Thus, the weight of the student is equal to the force that does the work on the student and the height of the staircase is the upward displacement. Suppose that Ben Pumpiniron elevates his kg body up the 2. If this were the case, then we could calculate Ben's power rating.

It can be assumed that Ben must apply an Newton downward force upon the stairs to elevate his body. By so doing, the stairs would push upward on Ben's body with just enough force to lift his body up the stairs. It can also be assumed that the angle between the force of the stairs on Ben and Ben's displacement is 0 degrees.

With these two approximations, Ben's power rating could be determined as shown below. This is shown below.

Work and Energy : Definition of Work in Physics

This new equation for power reveals that a powerful machine is both strong big force and fast big velocity. A powerful car engine is strong and fast. A powerful piece of farm equipment is strong and fast. A powerful weightlifter is strong and fast. A powerful lineman on a football team is strong and fast.

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A machine that is strong enough to apply a big force to cause a displacement in a small mount of time i. Use your understanding of work and power to answer the following questions. When finished, click the button to view the answers. Two physics students, Will N.