Introduction
Whenever a force acting on a body displaces it, work is said to be done. If a force F acting on the body displaces it by a displacement s in the direction of force then the work done is given by
W = F.s or W = |F||s|cos\[\Phi \]
where \[\Phi \] is the angle between the direction of force applied and the direction of displacement, W is the work done and is a vector quantity, therefore, work done can be positive or negative and it does not depend on the path followed and time taken.
The SI unit of work is the joule (J) and in the CGS system, the unit of work is erg.
1 joule = \[10^{7}\] erg
The SI unit of force is newton(N) and displacement is meter (m), therefore, J is also written as N.m. The MKS unit is kg \[m^{2} s^{-2}\] and in the CGS system, it is dyne-cm or erg.
Positive Work
If \[\Phi \] is acute (<90°), work done is positive as cos \[\Phi \] will be positive. For example, when a body free falls under gravity, \[\Phi \]=0, work done is positive.
Negative Work
If \[\Phi \]> 90°, work done is negative since cos\[\Phi \] will be negative. For example, when a ball is thrown up, its motion is opposed by gravity, \[\Phi \] between F and s is 180°.
Zero Work
When \[\Phi \]=90°, the work done is zero since cos 90° is 0. For example, when a coolie carries a bag, the force applied is in the upwards direction but the displacement is towards the forward direction making the angle between force and displacement be 90°. Therefore, even though energy is expended in exerting the force but work done W is zero.
Work done by Force
When \[\Phi \] is 0° then the direction of force and displacement are in the same direction and work done is simply given by
W = |F||s|
As stated already, when the direction of force is perpendicular to the direction of displacement, \[\Phi \] is 90° which makes work done W to be equal to 0.
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FAQs on Unit of Work
1. What are the Types of Work?
There are two types of work, namely, positive work and negative work.
Positive work
The work is described by the equation, W = FSCosӨ.
When Ө is acute i.e. Ө< 90° then work is said to be positive.
Examples
When a lawn roller is pulled by applying force along with the handle. The work done by the applied force F is positive.
Work done by the stretching force in spring is positive.
Negative work
It happens when Ө is obtuse i.e. Ө> 90°.
The angle between the force F and displacement S is 180°. Therefore, the work done by gravity on moving a body upwards is negative.
Examples
Rocket propulsion
Work done in pulling the load.
Pulling the water from the well.
Flying an airplane.
2. Write Some Real-Life Examples of Work.
There are certain real-life examples to describe the work.
Sitting in front of the laptop and typing something on it is the work.
When the road is busy, the force applied by a vehicle to slow down the speed is work.
The work done against the gravitational pull to escape an object from the earth.
The work done by the earth to rotate about its polar axis and around the Sun.
The work done by the pendulum to move to and fro when pulled from its rest position.
3. What is the S.I. unit of work?
The standard unit of work is the joule (J) which is also written as N.m as Newton (N) is the SI unit of force and meter (m) is the SI unit of displacement. The SI of the base unit is kg \[m^{2} s^{-2}\]. To know more about the SI unit of work jump onto Vedantu's website or download the app and get hold of free resources for your exam preparation! Download now!
4. What kind of work is done when a body is freely falling?
A body free-falling under the force of gravity is in the direction of the displacement of the body, therefore, the angle between force and displacement of the body ∅ is 0°. This makes the value of cos\[\Phi \] = 1 as cos 0° is 1. Therefore, work done by the body W is positive and is given as:
W= F.s where F is the force of gravity and s is the displacement of the body.
5. What are the factors affecting work?
There are two factors that affect work done on a body: the force applied on the body and the displacement of the body. Force can be defined as the push or pull on a body that causes it to change its velocity and acceleration. It is a vector quantity. Displacement of a body is defined as the shortest distance travelled by the body when force is applied. It is also a vector quantity.
6. How is work measured for gases?
Work done for gases is dependent upon the force exerted into a body containing the gas by the gas itself and the volume of the gas. For example, when gas is filled in a cylinder, the moving piston is allowed to expand. The work done in such a situation is given by:
W = P∆V where W is the work done in expanding the volume of the gas in the piston. In this case, work is a scalar quantity as work has a magnitude but no direction.