JEE and NEET CRASH COURSE

By, Ritesh Agarwal, B. Tech. IIT Bombay

WORKWork is said to be done by a force when theforce produces a displacement in the bodyon which it acts in any direction exceptperpendicular to the direction of the force.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Work is scalar quantityand can have +ve, -veor zero value.

Work done by Constant Force

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

ExampleCalculate the amount of work done in raising aglass of water weighing 0.5 kg through aheight of 20 cm. (g = 10 m/s2)

Sol. W = Force × distance= mgh = 0.5 × 10 × 0.2 = 1 J

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Work done by Variable Force

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

NOTE:- Area under force-displacement graph givesmagnitude of work done by the force.

ExampleA force F = (10 + 0.5x) N acts on a particle in xdirection, where x is in metre. Find the workdone by this force during a displacement fromx = 0 to x = 2.

Sol.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Work done by Several ForcesWhen several forces acts on a body thenthe net work done on the body is thealgebraic sum of work done by individualforce.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

PowerIt is defined as the rate at which the body can dothe work.

This power P is also called average power.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Instantaneous power (P)

Important PointsThe slope of work–time graph gives theinstantaneous power.

Area under power–time graph gives thework done.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

ExampleA pump can take out 7200 kg of water per hour from awell 100 m deep. Calculate the power of the pump,assuming that its efficiency is 50%. (g = 10 m/s2)

Sol.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Conservative ForceA force is said to be conservative if work done bythe force on a particle moving between two pointsdoes not depends on the path taken by the particle.

Examples

1. Gravitational force

2. Elastic force in a stretched or compressed spring

3. Electrostatic force

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Non-Conservative ForceA force is said to be non conservative, if work doneor against the force in moving a body from oneposition to another, depends on the path.

Examples

1. The velocity dependent forces such as : airresistance and viscous force

2. Retarding forces such as friction force and dragforce.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

EnergyEnergy is defined as the internal capacity for doingwork.When we say that a body has energy it mean that itcan do work.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Kinetic EnergyIf a particle of mass m is moving with velocity 'v'(much less than the velocity of the light) then thekinetic energy K.E. is given by

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

1. It is always non negative2. depends on the frame of reference

Work Energy TheoremAccording to this theorem work done by net forceon a body is equal to change in its kinetic energy.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

ExampleA bullet weighing 10 g is fired with a velocity 800 m/s.After passing through a mud wall 1m thick, its velocitydecreases to 100 m/s. Find the average resistanceoffered by the mud wall.Sol.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Potential Energy (P.E.)Definition 1:- Potential energy is the internalcapacity of doing work of a system by virtue of itsconfiguration.Definition 2:- The energy which a body has by virtueof its position or configuration in a conservativeforce field.Mathematical Definition:- Change in potentialenergy is negative of work done by internalconservative forces. ������ ������������ ������NOTE:- �������� ������������ ������

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Potential energy in different conservative fields(a) Gravitational P.E.:-Near the surface of earth assuming zero P.E. atearth’s surface

(b) Spring P.E.:- �� 2where, x is extension or compression in the spring

Work done by spring force = Ui - Uf

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

ExampleFind out work done by applied force to slowlyextend the spring from x to 2x.

Sol.Wapplied force = Wspring force

= Uf Ui

= �� 2 �� 2�� 2

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Relation between force and P.E.Force from P.E.If U(r); ����If U(x, y, z)

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

P.E. from Force

ExampleThe potential energy of a particle in a space isgiven by U = x2 + y2.Find the force associated with this potentialenergy.Sol.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Example

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Sol.

EquilibriumEquilibrium means; Fnet = 0Types of Equilibrium(a) Stable equilibriumIf on slight displacement from equilibriumposition a body has tendency to regain itsoriginal position.(b) Unstable equilibriumIf on slight displacement from equilibriumposition body moves in the direction ofdisplacement.(c) Neutral equilibriumIf on slight displacement from equilibriumposition a body has no tendency to comeback to original position or to move in thedirection of displacement.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Mechanical EnergySum of kinetic and potential energy

M.E. = K.E. + P.E.

• Scalar quantity

• S.I. Unit : Joule

• Depends on frame of reference

• M.E. ≥ P.E.

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)

Law of Conservation of Mechanical EnergyIf work done by non-conservative forces andexternal forces is zero, then M.E. of system willremain conserved.

MEinitial = MEfinal

KEinitial + PEinitial = KEfinal + PEfinal

Physics by Ritesh Agarwal (B. Tech. IIT Bombay)