Page 117 - Class-11-Physics-Part-1_Neat

LAWS OF MOTION 103

Answer As the string is inextensible, and the is the reason why discovery of the wheel has
pully is smooth, the 3 kg block and the 20 kg been a major milestone in human history.
trolley both have same magnitude of Rolling friction again has a complex origin,
acceleration. Applying second law to motion of though somewhat different from that of static
the block (Fig. 5.12(b)), and sliding friction. During rolling, the surfaces
30 – T = 3a in contact get momentarily deformed a little, and
this results in a finite area (not a point) of the
Apply the second law to motion of the trolley (Fig.
body being in contact with the surface. The net
5.12(c)),
effect is that the component of the contact force
T – f = 20 a.
k parallel to the surface opposes motion.
Now f = µ N,
k k We often regard friction as something
Here µ = 0.04,
k undesirable. In many situations, like in a
N = 20 x 10 machine with different moving parts, friction
= 200 N.
does have a negative role. It opposes relative
Thus the equation for the motion of the trolley is motion and thereby dissipates power in the form
T – 0.04 x 200 = 20 a Or T – 8 = 20a. of heat, etc. Lubricants are a way of reducing
kinetic friction in a machine. Another way is to
22 –2 -2
These equations give a = m s = 0.96 m s use ball bearings between two moving parts of a
23
and T = 27.1 N. t machine [Fig. 5.13(a)]. Since the rolling friction
between ball bearings and the surfaces in
Rolling friction contact is very small, power dissipation is
A body like a ring or a sphere rolling without reduced. A thin cushion of air maintained
slipping over a horizontal plane will suffer no between solid surfaces in relative motion is
another effective way of reducing friction (Fig.
friction, in principle. At every instant, there is 5.13(a)).
just one point of contact between the body and
In many practical situations, however, friction
the plane and this point has no motion relative
is critically needed. Kinetic friction that
to the plane. In this ideal situation, kinetic or
dissipates power is nevertheless important for
static friction is zero and the body should
quickly stopping relative motion. It is made use
continue to roll with constant velocity. We know, of by brakes in machines and automobiles.
in practice, this will not happen and some Similarly, static friction is important in daily
resistance to motion (rolling friction) does occur, life. We are able to walk because of friction. It
i.e. to keep the body rolling, some applied force is impossible for a car to move on a very slippery
is needed. For the same weight, rolling friction road. On an ordinary road, the friction between
is much smaller (even by 2 or 3 orders of the tyres and the road provides the necessary
magnitude) than static or sliding friction. This external force to accelerate the car.

Fig. 5.13 Some ways of reducing friction. (a) Ball bearings placed between moving parts of a machine.
(b) Compressed cushion of air between surfaces in relative motion.

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