what does doing work mean when it comes to physics

Learning Objectives

By the cease of this section, you volition be able to:

• Explain how an object must be displaced for a force on it to practise work.
• Explicate how relative directions of force and displacement make up one's mind whether the work done is positive, negative, or cipher.

What It Means to Practice Piece of work

The scientific definition of work differs in some means from its everyday meaning. Certain things nosotros think of as hard work, such as writing an test or carrying a heavy load on level ground, are not work as divers by a scientist. The scientific definition of piece of work reveals its human relationship to energy—whenever piece of work is done, energy is transferred.

For work, in the scientific sense, to be done, a forcefulness must be exerted and there must be motion or displacement in the direction of the force.

Formally, the work washed on a organization by a constant strength is defined to be the product of the component of the forcefulness in the direction of motion times the altitude through which the forcefulness acts. For one-style motion in one dimension, this is expressed in equation form asW = |F| (cosθ) |d|, where Due west is piece of work, d is the deportation of the organisation, and θ is the angle between the strength vector F and the deportation vector d, as in Figure ane. We can besides write this asW =Fd cosθ.

To find the work done on a system that undergoes move that is non one-way or that is in two or three dimensions, nosotros divide the motion into ane-way 1-dimensional segments and add up the piece of work done over each segment.

What is Work?

The work done on a system by a constant forcefulness is the production of the component of the force in the direction of movement times the distance through which the force acts. For ane-way motion in ane dimension, this is expressed in equation form equallyW =Fd cosθ, where Westward is work, F is the magnitude of the forcefulness on the system, d is the magnitude of the displacement of the system, and θ is the bending between the force vector F and the deportation vector d.

Figure 1. examples of piece of work. (a) The work washed by the forcefulness F on this lawn mower isFd cosθ. Note thatF cosθ is the component of the force in the direction of motion. (b) A person holding a briefcase does no work on it, because there is no movement. No free energy is transferred to or from the briefcase. (c) The person moving the briefcase horizontally at a abiding speed does no work on it, and transfers no free energy to information technology. (d) Work is washed on the briefcase by carrying information technology upward stairs at abiding speed, because at that place is necessarily a component of force F in the management of the movement. Energy is transferred to the briefcase and could in turn be used to do work. (e) When the briefcase is lowered, energy is transferred out of the briefcase and into an electrical generator. Here the work done on the briefcase by the generator is negative, removing energy from the briefcase, because F and d are in reverse directions.

To examine what the definition of work means, let us consider the other situations shown in Effigy 1. The person belongings the briefcase in Figure 1b does no piece of work, for example. Hither d = 0, so W = 0. Why is it y'all become tired just holding a load? The reply is that your muscles are doing work against ane another, but they are doing no work on the system of interest (the "briefcase-Earth organization"—meet Gravitational Potential Energy for more than details). There must be movement for work to be washed, and in that location must be a component of the force in the management of the motion. For instance, the person conveying the briefcase on level ground in Figure 1c does no piece of work on it, because the force is perpendicular to the motility. That is, cos 90º = 0, and then W = 0.

In contrast, when a forcefulness exerted on the arrangement has a component in the direction of motion, such as in Effigy 1d, work is done—energy is transferred to the briefcase. Finally, in Figure 1e, free energy is transferred from the briefcase to a generator. In that location are two adept ways to translate this energy transfer. Ane interpretation is that the briefcase'due south weight does work on the generator, giving information technology energy. The other estimation is that the generator does negative work on the briefcase, thus removing energy from it. The drawing shows the latter, with the strength from the generator upwardly on the briefcase, and the displacement downward. This makes θ = 180º, and cos 180º = −1; therefore, Due west is negative.

Computing Work

Work and free energy have the same units. From the definition of work, we come across that those units are force times altitude. Thus, in SI units, work and energy are measured in newton-meters. A newton-meter is given the special name joule (J), and 1J = 1N · m = ane kg · m²/s^two. One joule is not a large amount of energy; it would lift a small 100-gram apple tree a altitude of virtually 1 meter.

Example i. Calculating the Piece of work You Practise to Push a Lawn Mower Across a Large Lawn

How much piece of work is done on the backyard mower past the person in Figure 1a if he exerts a constant force of 75.0 North at an angle 35º below the horizontal and pushes the mower 25.0 m on level ground? Convert the amount of work from joules to kilocalories and compare it with this person'southward average daily intake of x,000 kJ (virtually 2400 kcal) of food energy. One calorie (1 cal) of heat is the amount required to warm i grand of h2o by 1ºC, and is equivalent to 4.184 J, while ane food calorie (i kcal) is equivalent to 4184 J.

Strategy

We can solve this problem by substituting the given values into the definition of work washed on a system, stated in the equation Due west =Fd cosθ. The force, angle, and displacement are given, so that only the piece of work West is unknown.

Solution

The equation for the work isW =Fd cosθ.

Substituting the known values gives

[latex]\begin{array}{lll}Westward&=&(75.0\text{ N})(25.0\text{ m})\cos(35.0^{\circ})\\\text{ }&=&1536\text{ J}=1.54\times10^3\text{ J}\end{assortment}\\[/latex]

Converting the work in joules to kilocalories yields W = (1536 J)(one kcal/4184 J) = 0.367 kcal. The ratio of the piece of work washed to the daily consumption is

[latex]\displaystyle\frac{W}{2400\text{ kcal}}=1.53\times10^{-iv}\\[/latex]

Discussion

This ratio is a tiny fraction of what the person consumes, but it is typical. Very little of the free energy released in the consumption of food is used to do work. Fifty-fifty when nosotros "work" all twenty-four hour period long, less than 10% of our food energy intake is used to exercise work and more ninety% is converted to thermal energy or stored as chemical energy in fat.

Section Summary

Work is the transfer of energy by a force acting on an object as information technology is displaced.

The work West that a force F does on an object is the product of the magnitude F of the strength, times the magnitude d of the displacement, times the cosine of the bending θ between them. In symbols,W =Fd cosθ.

The SI unit for work and energy is the joule (J), where 1 J = ane N ⋅ grand = 1 kg ⋅ m²/southⁱⁱ.

The work done past a strength is zero if the displacement is either cypher or perpendicular to the force.

The work done is positive if the force and displacement have the aforementioned direction, and negative if they have opposite management.

Conceptual Questions

1. Give an example of something we call back of every bit work in everyday circumstances that is not work in the scientific sense. Is free energy transferred or inverse in form in your case? If then, explicate how this is accomplished without doing work.
2. Give an example of a state of affairs in which in that location is a force and a displacement, simply the forcefulness does no work. Explain why it does no piece of work.
3. Describe a state of affairs in which a force is exerted for a long time but does no piece of work. Explain.

Problems & Exercises

1. How much work does a supermarket checkout attendant do on a can of soup he pushes 0.600 m horizontally with a force of five.00 N? Express your answer in joules and kilocalories.
2. A 75.0-kg person climbs stairs, gaining two.50 meters in height. Discover the piece of work done to accomplish this task.
3. (a) Summate the piece of work washed on a 1500-kg lift car by its cable to lift it 40.0 m at constant speed, bold friction averages 100 N. (b) What is the work done on the elevator by the gravitational force in this process? (c) What is the total work done on the lift?
4. Suppose a car travels 108 km at a speed of 30.0 yard/due south, and uses 2.0 gal of gasoline. Only 30% of the gasoline goes into useful work by the force that keeps the car moving at constant speed despite friction. (A gallon of gasoline has one.2 × 10⁸ J.) (a) What is the magnitude of the strength exerted to keep the car moving at abiding speed? (b) If the required force is directly proportional to speed, how many gallons volition be used to drive 108 km at a speed of 28.0 m/s?
5. Calculate the piece of work done by an 85.0-kg homo who pushes a crate four.00 m upwardly along a ramp that makes an angle of 20.0º with the horizontal. (See Effigy 2.) He exerts a forcefulness of 500 N on the crate parallel to the ramp and moves at a constant speed. Be certain to include the work he does on the crate and on his body to get up the ramp.

   

   Figure 2. A human pushes a crate up a ramp.

6. How much work is washed by the boy pulling his sister thirty.0 m in a wagon as shown in Figure 3? Assume no friction acts on the wagon.

   

   Figure iii. The boy does work on the system of the carriage and the child when he pulls them as shown.

7. A shopper pushes a grocery cart xx.0 m at constant speed on level ground, against a 35.0 N frictional force. He pushes in a direction 25.0º beneath the horizontal. (a) What is the work washed on the cart by friction? (b) What is the work done on the cart by the gravitational force? (c) What is the work done on the cart by the shopper? (d) Find the strength the shopper exerts, using free energy considerations. (east) What is the total work washed on the cart?
8. Suppose the ski patrol lowers a rescue sled and victim, having a full mass of xc.0 kg, down a 60.0º slope at constant speed, equally shown in Figure 4. The coefficient of friction between the sled and the snowfall is 0.100. (a) How much piece of work is done by friction as the sled moves 30.0 chiliad along the loma? (b) How much work is done by the rope on the sled in this distance? (c) What is the work washed by the gravitational force on the sled? (d) What is the total piece of work done?

   

   Figure 4. A rescue sled and victim are lowered downwards a steep gradient.

Glossary

energy:the ability to practise work

work: the transfer of energy by a force that causes an object to be displaced; the product of the component of the force in the direction of the displacement and the magnitude of the displacement

joule: SI unit of work and free energy, equal to one newton-meter

Selected Solutions to Problems & Exercises

1. 3.00 J = 7.17 × 10⁻⁴ kcal

3. (a) 5.92 × 10⁵ J; (b) −5.88 × 10⁵ J; (c) The net strength is zero.

5. three.xiv × 10^three J

7.  (a) −700 J; (b) 0; (c) 700 J; (d) 38.6 N; (e) 0

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