For work to be done, a force must be exerted and there must be motion or displacement in the direction of the force. The work done by a force acting on an object is equal to the magnitude of the force multiplied by the distance moved in the direction of the force. Work has only magnitude and no direction. Hence, work is a scalar quantity.
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The work done by a force is defined to be the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
\(\begin{array}{l}W=F\cos\Theta=\vec{F}\vec{d}\end{array} \)
Where W is the work done, F is the force, d is the displacement, θ is the angle between force and displacement and F cosθ is the component of force in the direction of displacement.
We understand from the work equation that if there is no displacement, there is no work done, irrespective of how large the force is. To summarize, we can say that no work is done if:
The SI unit of work is Joule (J). For example, if a force of 5 newtons is applied to an object and moves 2 meters, the work done will be 10 newton-meter or 10 Joule. It should be noted that 1 J = 1 N ⋅ m = 1 kg ⋅ m2/s2.
An object is horizontally dragged across the surface by a 100 N force acting parallel to the surface. Find out the amount of work done by the force in moving the object through a distance of 8 m.
Solution:
Given:
F = 100 N, d = 8 m
Since F and d are in the same direction, θ = 0, [θ is the angle of the force to the direction of movement], therefore
W = FdCos θ
W = 100 x 8 x Cos 0
W = 800 J [Since Cos 0 = 1]
Energy is the ability to perform work. Energy can neither be created nor destroyed, and it can only be transformed from one form to another. The unit of Energy is the same as of Work, i.e. Joules. Energy is found in many things, and thus there are different types of energy.
All forms of energy are either kinetic or potential. The energy in motion is known as Kinetic Energy, whereas Potential Energy is the energy stored in an object and is measured by the amount of work done.
Some other types of energy are given below:
The SI unit of energy is Joules (J), named in honour of James Prescott Joule.
Power is a physical concept with several different meanings, depending on the context and the available information. We can define power as the rate of doing work, and it is the amount of energy consumed per unit of time.
As discussed, power is the rate of doing work. Therefore, it can be calculated by dividing work done by time. The formula for power is given below.
\(\begin{array}{l}P = \frac{W}{t}\end{array} \)
Where, P is the power, W is the work done and t is the time taken.
As power doesn’t have any direction, it is a scalar quantity. The SI unit of power is Joules per Second (J/s), which is termed as Watt. Watt can be defined as the power needed to do one joule of work in one second. The unit Watt is dedicated in honour of Sir James Watt, the developer of the steam engine.
Read the article below to learn the SI unit of power in detail.
Unit of Power
A garage hoist lifts a truck up 2 meters above the ground in 15 seconds. Find the power delivered to the truck. [Given: 1000 kg as the mass of the truck]
First we need to calculate the work done, which requires the force necessary to lift the truck against gravity:
F = mg = 1000 x 9.81 = 9810 N.
W = Fd = 9810N x 2m = 19620 Nm = 19620 J.
The power is P = W/t = 19620J / 15s = 1308 J/s = 1308 W.
Here is an engaging video explanation of Work, Energy and Power and the relationship between them.
W = F × d
Unit The SI unit of work is the Joule (J)P.E. = mgh
Unit The SI unit of energy is Joules (J).P = W/t
Unit The SI unit of power is Watt (W).Frequently Asked Questions
Q1
Work is the energy needed to apply a force to move an object a particular distance. Power is the rate at which that work is done.
Q2
The unit of work is Joule.
Q3
The unit of energy is Joule.
Q4
The unit of power is Watt.
Q5
Power is a scalar quantity because it is a ratio of two scalar quantities.
Watch this fun and engaging rapid fire session based on the topic Work, Energy and Power!Work, Power and Energy is one of the important topics of JEE Main and JEE Advanced, watch the video and understand the type of questions asked from this topic!
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By the end of this section, you will be able to do the following:
Use the lab titled Work and Energy as a supplement to address content in this section.
calculate the mechanical energy of, power generated within, impulse applied to, and momentum of a physical system.
The learning objectives in this section will help your students master the following standards:
[AL][AL] Remind students of the equation W = P E e = f m g W = P E e = f m g . Point out that acceleration due to gravity is a constant, therefore PE e that results from work done by gravity will also be constant. Compare this to acceleration due to other forces, such as applying muscles to lift a rock, which may not be constant.
[BL][OL] Review understanding of mass, velocity, and acceleration due to gravity. Define the general definitions of the words potential and kinetic.
In this section, students learn how work determines changes in kinetic energy and that power is the rate at which work is done.
In physics, the term work has a very specific definition. Work is application of force, ff, to move an object over a distance, d, in the direction that the force is applied. Work, W, is described by the equation
W=fd. W=fd.
Some things that we typically consider to be work are not work in the scientific sense of the term. Let’s consider a few examples. Think about why each of the following statements is true.
The first two examples are fairly simple. Homework is not work because objects are not being moved over a distance. Lifting a rock up off the ground is work because the rock is moving in the direction that force is applied. The last example is less obvious. Recall from the laws of motion that force is not required to move an object at constant velocity. Therefore, while some force may be applied to keep the rock up off the ground, no net force is applied to keep the rock moving forward at constant velocity.
Teacher Support
Teacher Support
[BL][OL] Explain that, when this theorem is applied to an object that is initially at rest and then accelerates, the 1 2 m v 1 2 1 2 m v 1 2 term equals zero.
[OL][AL] Work is measured in joules and W=fd W=fd . Force is measured in newtons and distance in meters, so joules are equivalent to newton-meters ( N⋅m ) ( N⋅m )
Work and energy are closely related. When you do work to move an object, you change the object’s energy. You (or an object) also expend energy to do work. In fact, energy can be defined as the ability to do work. Energy can take a variety of different forms, and one form of energy can transform to another. In this chapter we will be concerned with mechanical energy, which comes in two forms: kinetic energy and potential energy.
Gravitational potential energy
is the stored energy an object has as a result of its position above Earth’s surface (or another object in space). A roller coaster car at the top of a hill has gravitational potential energy.Let’s examine how doing work on an object changes the object’s energy. If we apply force to lift a rock off the ground, we increase the rock’s potential energy, PE. If we drop the rock, the force of gravity increases the rock’s kinetic energy as the rock moves downward until it hits the ground.
The force we exert to lift the rock is equal to its weight, w, which is equal to its mass, m, multiplied by acceleration due to gravity, g.
f=w=mg f=w=mg
The work we do on the rock equals the force we exert multiplied by the distance, d, that we lift the rock. The work we do on the rock also equals the rock’s gain in gravitational potential energy, PEe.
W=P E e =mgd W=P E e =mgd
Kinetic energy depends on the mass of an object and its velocity, v.
KE= 1 2 m v 2 KE= 1 2 m v 2
When we drop the rock the force of gravity causes the rock to fall, giving the rock kinetic energy. When work done on an object increases only its kinetic energy, then the net work equals the change in the value of the quantity 1 2 m v 2 1 2 m v 2 . This is a statement of the work–energy theorem, which is expressed mathematically as
W=ΔKE = 1 2 m v 2 2 − 1 2 m v 1 2 . W=ΔKE = 1 2 m v 2 2 − 1 2 m v 1 2 .
The subscripts 2 and 1 indicate the final and initial velocity, respectively. This theorem was proposed and successfully tested by James Joule, shown in Figure 9.2.
Does the name Joule sound familiar? The joule (J) is the metric unit of measurement for both work and energy. The measurement of work and energy with the same unit reinforces the idea that work and energy are related and can be converted into one another. 1.0 J = 1.0 N∙m, the units of force multiplied by distance. 1.0 N = 1.0 kg∙m/s2, so 1.0 J = 1.0 kg∙m2/s2. Analyzing the units of the term (1/2)mv2 will produce the same units for joules.
Figure
9.2
The joule is named after physicist James Joule (1818–1889). (C. H. Jeens, Wikimedia Commons)
Watch Physics
Work and Energy
This video explains the work energy theorem and discusses how work done on an object increases the object’s KE.
Access multimedia contentGrasp Check
True or false—The energy increase of an object acted on only by a gravitational force is equal to the product of the object's weight and the distance the object falls.
Teacher Support
Teacher Support
Repeat the information on kinetic and potential energy discussed earlier in the section. Have the students distinguish between and understand the two ways of increasing the energy of an object (1) applying a horizontal force to increase KE and (2) applying a vertical force to increase PE.
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