2019-03-01_Physics_Times

(II) Motion of a vehicle on a smooth banked road:

Here Nsin balances the weight of vehicle.

Ncosmg (i)

The other component Nsin is directed

towards the centre of the circular path which

provides the centripetal force.

2

sin

mv

N

r

 (ii) From eq’s (i) & (ii) we get,

2

tan

v

rg



 v rgtan

5. Work, Power & Energy

Work done by the force is measured as the product
of displacement and the component of force in
the direction of displacement.

Work done by force may be positive, negative or

zero.

(I) Positive Work

W F cosS FS cosF S.



Work is a scalar quantity.

Dimensional formula of work is
ML T .2 2
Its S.I Unit is N-m or Joule (J)
The work done by a constant force acting on
the body when its displacement ‘S’ is given by
W FS maS 
If force displaces the particle from its initial position

ri



to final position rf



then displacement vector

S r r f i

  

W F S F r r.  . fi

   

W FS cos

= positive, when 0   90 

(II) Negative Work

W FS( cos )

= negative, when 90   180 .

(III) Zero Work

If a body is displaced perpendicular to the

direction of force then work done is zero

^90 

 

If there is no displacement [S=0] then work

done is zero.

When several constant forces simultaneously

act on a body and if the total displacement is S



net work done on the body is

W W W Wnet    1 2 3 ........

Force - Displacement Graph

In the graph shown the work done by the

force on a body that displaces from x xito f

is equal to area of the shaded portion.

The area of the graph is equal to

2

1

x

x

F dx

1. Work done by a Constant Force

2. Nature of Work

3. Work done by Multiple constant Forces