Page 131 - Class-11-Physics-Part-1_Neat

WORK, ENERGY AND POWER 117

The work done by the force is defined to be Table 6.1 Alternative Units of Work/Energy in J
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 (6.4)
We see that 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 t Example 6.3 A cyclist comes to a skidding
your muscles are alternatively contracting and stop in 10 m. During this process, the force
relaxing and internal energy is being used up on the cycle due to the road is 200 N and
and you do get tired. Thus, the meaning of work is directly opposed to the motion. (a) How
in physics is different from its usage in everyday much work does the road do on the cycle ?
language. (b) How much work does the cycle do on
the road ?
No work is done if :
(i) the displacement is zero as seen in the
example above. A weightlifter holding a 150 Answer Work done on the cycle by the road is
kg mass steadily on his shoulder for 30 s the work done by the stopping (frictional) force
does no work on the load during this time. on the cycle due to the road.
(ii) the force is zero. A block moving on a smooth (a) The stopping force and the displacement make
horizontal table is not acted upon by a an angle of 180 o (π rad) with each other.
horizontal force (since there is no friction), but Thus, work done by the road,
may undergo a large displacement. W = Fd cosθ
r
(iii) the force and displacement are mutually = 200 × 10 × cos π
perpendicular. This is so since, for θ = π/2 rad
(= 90 ), cos (π/2) = 0. For the block moving on = – 2000 J
o
a smooth horizontal table, the gravitational It is this negative work that brings the cycle
to a halt in accordance with WE theorem.
force mg does no work since it acts at right
(b) From Newton’s Third Law an equal and
angles to the displacement. If we assume that
the moon’s orbits around the earth is opposite force acts on the road due to the
perfectly circular then the earth’s cycle. Its magnitude is 200 N. However, the
road undergoes no displacement. Thus,
gravitational force does no work. The moon’s
instantaneous displacement is tangential work done by cycle on the road is zero. t
while the earth’s force is radially inwards and The lesson of Example 6.3 is that though the
θ = π/2. force on a body A exerted by the body B is always
Work can be both positive and negative. If θ is equal and opposite to that on B by A (Newton’s
between 0 and 90 , cos θ in Eq. (6.4) is positive. Third Law); the work done on A by B is not
o
o
o
o
If θ is between 90 and 180 , cos θ is negative. necessarily equal and opposite to the work done
In many examples the frictional force opposes on B by A.
o
displacement and θ = 180 . Then the work done
6.4 KINETIC ENERGY
o
by friction is negative (cos 180 = –1).
As noted earlier, if an object of mass m has
From Eq. (6.4) it is clear that work and energy
velocity v, its kinetic energy K is
–2
2
have the same dimensions, [ML T ]. The SI unit
of these is joule (J), named after the famous British 1 1
2
physicist James Prescott Joule (1811-1869). Since K = m v v = mv (6.5)
.
work and energy are so widely used as physical 2 2
concepts, alternative units abound and some of Kinetic energy is a scalar quantity. The kinetic
these are listed in Table 6.1. energy of an object is a measure of the work an

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