Physics Complete: WORK

Showing posts with label WORK. Show all posts

Work Energy Theorem

The applied force on a body is able to produce displacement then work is said to be done. The work done by a force is stored in the form of kinetic energy.

The work done is a scalar having only magnitude but not any specific direction.

The work done by a variable force can be determined as shown below. Let us consider only one dimensional motion of the body.

Different Theories of Light and Their Analysis

Representation of Light as Wave

Interference of Light an Overview

Fringe Width and Angular Fringe Width in Interference

Interference Fringe shift and Problems

Polarization Concepts and Problems

Diffraction in Wave Optics Overview

Resolving Power of Optical Instruments

Common Forces in mechanics
Free body diagram
Circular motion part one and two

Work done by variable Force

A constant force is rare. It is the variable force, which is more commonly encountered. Fig. a below is a plot of a varying force in one dimension. If the displacement Δx is small, we can take the force F (x) as approximately constant and the work done is then ΔW =F (x) Δx .

If the displacements are allowed to approach zero, then the number of terms in the sum increases without limit, but the sum approaches a definite value equal to the area under the curve in Fig. b Then the work done can be determined as shown below.

where ‘lim’ stands for the limit of the sum when Δx tends to zero. Thus, for a varying force the work done can be expressed as a definite integral of force over displacement .

Different Theories of Light and Their Analysis

Representation of Light as Wave

Interference of Light an Overview

Fringe Width and Angular Fringe Width in Interference

Interference Fringe shift and Problems

Polarization Concepts and Problems

Diffraction in Wave Optics Overview

Resolving Power of Optical Instruments

Work

Work is said to be done when applied force is able to produce displacement in a body.

Consider a constant force F acting on an object of mass m. The object undergoes a displacement d in the positive x-direction as shown in Fig.

The work done by the force is defined to be the product of component of the force in the direction of the displacement and the magnitude of this displacement. Thus W = (F cos θ )d = F.d

If there is no displacement, there is no work done even if the force is large. Thus, when you push hard against a rigid brick wall, the force you exert on the wall does no work. Yet your muscles are alternatively contracting and relaxing and internal energy is being used up and you do get tired. Thus, the meaning of work in physics is different from its usage in everyday language.

No work is done if :

(1) The displacement is zero . A weightlifter holding a 150 kg mass steadily on his shoulder for 30 s does no work on the load during this time.

(2) The force is zero. A block moving on a smooth horizontal table is not acted upon by a horizontal force (since there is no friction), but may undergo a large displacement.

(3) the force and displacement are mutually perpendicular. This is so since, for θ = π/2 rad , cos (π /2) = 0. For the block moving on a smooth horizontal table, the gravitational force mg does no work since it acts at right angles to the displacement.

If we assume that the moon’s orbits around the earth is perfectly circular then the earth’s gravitational force does no work. The moon’s instantaneous displacement is tangential while the earth’s force is radially inwards and θ = π/2.

Work can be both positive and negative. If θ is between 0 and 90, cos θ is positive. If θ is between 90 and 180, cos θ is negative. In many examples the frictional force opposes displacement and θ = 180. Then the work done by friction is negative (cos 180 = –1).

The work and energy have the same dimensions. The SI unit of these is joule (J).

The following are different system of units.