# Work and Energy: Brief Introduction | Physics Grade XI

### Work and Energy # Brief Introduction to Work and Energy

Introduction

Work done is defined as the product of the distance traveled by a body when force is applied in any direction except perpendicular to force.

Work done by a constant force is defined as the displacement produced by a constant force when it acts on a body. If θ is the angle between F and s as shown in the figure (B), then from equation(I) we have

W = F. s.cosθ …………(II)

If displacement and the force is in the same direction as shown in figure(I), then θ = 0, cosθ = 1,

W = F. s. 1

=F. s

Units of works

1J = 1N * 1m = 105 dyne * 100cm = 107 erg

Work done by Variable force

Let a variable force is acting on a body to displace it from A to B in a fixed direction. We can consider the entire displacement from A to B is made up of a large number of infinitesimal displacements. One such displacement is shown in the figure from P to Q. As the displacement PQ = dx is infinitesimally small, we consider that along with the displacement, force is constant in magnitudes as well as in direction. Small amount of work done in moving a body from P to Q is

dW = F * dx = (PS) (PQ) = area of strip PQRS

Total work done in moving body from A to B is given by,

W = ∑dW = ∑F. dx

If the displacements are allowed to approach zero, then the number f terms in the sum increases without limit. And sum approaches a definite value equal to the area under the curve CD as shown in the figure.

Hence, we can write

W = lim dx -> 0   ∑f (dx)

= xbʃxa F dx

=xbʃxa area of strip PQRS

= total area under the curve between F and x-axis from x = xA to x= xB

W = Area ABCDA

Hence work done by a variable force is numerically equal to the area under the force curve and the displacements.

Energy is defined as the capacity to do work.

Kinetic Energy is the energy possessed by a body due to its motion.

Expression for Kinetic Energy

Let us consider a block of mass lying on a smooth horizontal surface as shown in figure. Let a constant force F be applied on it such that, after traveling a distance s, its velocity becomes v. If a be the acceleration of the body, then

V2 = u2 + 2as = 0 + 2as

Or, v2 = 2as

as initial velocity, u = 0,

So,     as = v2/ 2 …………… (i)

As workdone on the body = force * distance, then

W = F * s

= m. a. s   ………………. (ii)

From equations (i) and (ii), we have

W = m * v2/2      [as = v2/ 2]

= ½ mv2     is the expression for Kinetic Energy of a body

Potential Energy is the energy possessed by a body due to its position or configuration.

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