Concept of Work

In physics, work is said to be done when a force is acting on a body, provided the body is placed in any direction except in a direction perpendicular to the direction of the force.

Dimensions and units of work are ML2T-2.

The units of work are of two kinds:

The SI unit of the work is Joule (J). Whereas in the CGS system, the unit of work is erg. The dimensional formula of work is ML2T-2

1. a) Absolute units
2. i) Joule: It is the SI system of units. The work done is said to be 1 joule, when a work done by a force of 1 newton causes a displacement of 1 meter in the direction of applied force.

1 joule = 1 newton × 1 meter × cos00 = 1N.m

1. ii) Erg: It is the absolute unit of work in the CGS system of units. The work done is said to be 1 erg, when a work done by a force of 1 dyne causes a displacement of 1 cm in the direction of applied force.

1erg = 1dyne × 1cm × cos00 = 1 dyne.cm

1. b) Gravitational units

These are also known as functional units of work.

1. i) Kilogram-meter (kg-m)
2. ii) Gram-centimeter (g-cm)

 Work Done by a constant force

When a force acting on a body produces a displacement in the body, then the work done by the force (W), i.e., W = FS Cos Ø.

Here F is constant force

S is displacement to due to force

Ø is angle between force and displacement

Factors Affecting Work

The factors that are affecting the work are:

•  Force – It is defined as a push or a pull that can cause any object with a mass to change its velocity and acceleration.
•  Displacement – The angle between the force vector and the displacement vector.

Conservation and Non – conservation Forces

Conservative forces: A force is said to be conservative if the total work done by or against a moving particle between two points is independent of the path taken.Ex: Earth’s gravitational force is an example of a conservative force, whereas frictional force is an example of a non-conservative force.

Examples of non-conservative forces are Air Resistance, Friction, and Tension in the cord.

As word done W = F.S = F S Cos Ø

Earth’s gravitational force F =  mg and the object is at height h. Since the object will fall down due to gravitational force so the angle between force and displacement will be 0 degree.

Therefore work done W = (mg) h cos 0° = mgh

Properties of conservation forces

1) The work done by or against the force on a moving body only depends on the initial and final position irrespective of the path taken by the body.

2) The work done by a conservative force is always reversible.

3) In any closed path, the work done by or against a conservative force in a moving body is always 0.

Non-conservation forces

A force is non-conservative if work done by or against the force in moving a body from one position to another depends on the path between these two positions.

 Nature of Work done

1) Positive Work

Work is a scalar quantity that may be positive or negative or even 0 as given below:

W = FS Cos Ø

Where Ø is acute (< 90°), cos Ø is positive, so work done is positive.

Ex:

1.  When a body falls freely under gravity, Ø = 0°, cos Ø = cos 0° = + 1 so the body falling freely is +ve.
2.  When a bull pulls a cart by applying a force along the rope at an acute angle, work done by the applied force is +ve.
3. When a spring is stretched, work done by the stretching force is +ve.

 2) Negative Work

W = F S Cos Ø

Where Ø is acute (> 90°), cos Ø is negative, so work done is negative.

Ex: When a body is thrown up, its motion is opposed by gravity

Energy

It is defined as the capacity or ability of the body to do the work. If a body is capable of doing more work, it is said to possess more energy.

Dimensions and units of work are M1L2T−2

 The units measurement of energy is the joule, and c.g.s system, the unit of energy is erg.

Work Energy

Work energy as per the principle, work done by a force in displacing a body measures the change in kinetic energy of the body.

When a force does some work on a body, the Kinetic energy of the body increases by the same amount. When an opposing force is applied to a body, its kinetic energy decreases. As per the work-energy principle, work and kinetic energy are equivalent quantities.

W = change in K.E of the body

1. Work done on a body may also be stored in the body in the form of potential energy.
2. When the KE of a body decreases, work done on the body must be negative and vice-versa.
3. Work energy theorems are true for any system of particles in the presence of all types of forces. These forces may be conservative or non-conservative.
4. When we consider a system of particles and the particles exert forces on one another, then change in K.E. of the system is equal to work done on the system by the external and internal forces.

Conclusion

Work definition in physics is the measure of energy transfer that occurs when an object is moved over a distance by an external force. Work done in compressing gas at constant temperature ay be expressed as

W= PdV

Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.