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Study Material for Class 11 Physics Chapter 6 Work Energy and Power
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Class 11 Physics Chapter 6 Work Energy and Power
WORK
If a constant force F displaces a body through displacement s then the work done, W, is given by
W= Fscos θ =F.s
Where s is magnitude of displacement and θ is angle between force and displacement
S.I. unit of work is Joule or Newton-metre.
If the work is done by a variable force F which displaces body from position A to B; having respective
position vectors r1 and r2 , the work WAB is given by
where ds is a small displacement of the body between A and B. Work is a scalar quantity. If a number of forces are acting, the total work on the body is equal to the sum of the work done by all the forces.
SIGN CONVENTION OF WORK
When 0 < θ < 90°
i.e., when the force supports the motion of the body, work done by that force is said to positive but when ∏/2<θ≤∏
i.e. in this case force opposes the motion of the body and so work done by that force is said to be negative.
If a spring of spring constant k is stretched from initial extension xi to final extension xf, then the force opposes extension such that F = –kx. The work dW done in extending the spring through dx is given by
The work done by a spring force is negative. Force of friction also does some work which can be negative, zero or positive depending upon whether the friction force is opposing motion, causing no relative motion between surfaces and friction force is supporting the motion respectively.
ENERGY
The energy of a body is the capacity of the body to do the work. It is a scalar quantity with the same unit as that for work (Joule in S.I. unit). In mechanics, kinetic and potential energies are involved with the dynamics of the body.
KINETIC ENERGY
It is the energy possessed by a body by virtue of its motion. A body of mass m moving with a velocity v has a kinetic energy, Ek=1/2mv2.
since velocity is a relative parameter so KE is also a relative parameter
TYPES OF FORCES
CONSERVATIVE AND NON-CONSERVATIVE FORCES
A force is said to be conservative if the work done by the force in moving a particle from one point to another point does not depend upon the path taken but depends upon the initial and final positions. The work done by a conservative force around a closed path is zero. Gravitational force, electric force, spring force etc. are examples of conservative forces. All central forces are conservative forces. If the work done by a force in moving a body from one point to another point depends upon the path followed, then the force is said to be non-conservative. The work done by such a force in moving a particle around a closed path is not zero. For example, the frictional forces and viscous forces works in an irreversible manner and a part of energy is lost in overcoming these frictional forces (Mechanical energy is converted to other energy forms such as heat, sound etc.). Therefore these are non-conservative forces.
POTENTIAL ENERGY
It is the energy of a body possesed by virtue of its position or the energy possessed by the body due to its state.
It is independent of the way in which body is taken to this state. It is a relative parameter and depends upon its value at reference level.
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