97

Friction

OBJECTIVE II

at F, F,and f denote the magnitudes of the

rce. normal force and the contact (c) Limiting friction is always greater than the kinetic
friction exerted by one friction.
eurface on the other kept in
contact. If none of these is
zero, (d) Limiting friction is never less than static friction.

(a) F> FN (b) F>f (e) F >f

(d) FN-f<F<F, +f. 4. A block is placed on a rough floor and a horizontal force

on it. The force of friction f by the floor on

Mhe contact force exerted by a
body A on another body
F is applied

D is equal to the the block is measured for different values of F and a

normal force between the
bodieg, We graph is plotted between them.
conclude that
(a)the surfaces must be frictionless (a) The graph is a straight line of slope 45.
h)the force of friction between (b) The graph is a straight line parallel to ue F-axis.
the bodies is zero
io the magnitude of normal (c) The graçh is a straight line of slope 45° for small F
a the bodies may be rough
force equals that of friction
but they don't slip on each
and a straight line parallel to the F-axis for large F.
other.
(d) There is a small kink on the graph.

Merk the correct statements 5. Consider a vehicle going on a horizontal road towards
about the friction between
bodies. east. Neglect any force by the air. The frictional forces
two
io) Static friction is always on the vehicle by the road
greater than the kinetic (a) is towards east if the vehicle is accelerating
friction.
) Coefficier& of static friction is
always greater than
(b) is zero if the vehicle is moving with a uniform velocity
the coefficient (c) must be towards east
of kinetic friction.
(d) must be towards west.

EXERCISES

1. A body slipping on a rough

horizontal plane moves with
a deceleration of 4-0 m/s. What is
the coefficient of
kineticfriction between the block
and the plane ?
2. Å block is projected along
a rough horizontal road with
a speed of 10 m/s. If the coefficient of kinetic friction is
0-10, how far will it travel before coming to rest ? A45

3. A block of mass m is kept ona horizontal table. If the

Figure 6-E1
static friction coefficient is u, find the frictional force

acting on the block.

4. A block slides down an inclined surface of inclination 9. A body starts slipping down an incline and moves half
30° with the horizontal. Starting from rest it covers 8 m meter in half second. How long will it taketo move the

in the first two seconds. Find the coefficient of kinetic next half meter?
friction between the two.
10. The angle between the resultant contact force and the
5. Suppose the block of the previous problem is pushed normal force exerted by a body on the other is called the
down the incline with a force of 4 N. How far will the
angle of friction. Show that, if A be the angle of friction
block move in the first two seconds after starting from and the coefficient of static friction, astan.
rest ? The mass of the block, is 4 kg.
11. Consider the situation shown in figure (6-E2). Calculate
6. A body of mass 2 kg is lying on a rough inclined plane
(a) the acceleration of the 1-0 kg blocks, (b) the tension
of inclination 30°. Find the magnitude of the force
in the string connecting the l0
kg blocks and (c) the
parallel to the incline needed to make the block move tension in the string attached to 0-50 kg.
(a) up the incline (b) down the incline. Coefficient of
static friction = 0-2.
1.0 kg 1.0 kg

7. Repeat part (a) of problem 6 if the push is applied

horizontally and not parallel to the incline.

u=0.2 u=0.2
8. In a children-park an inclined plane is constructed with
an angle of incline 45° in the middle part figure 6-E1).
Find the acceleration of a boy sliding on it if the friction
coefficient between the cloth of the boy and the incline
is 0-6 and g =10m/s 2
02oe k Figure 6-E2
 98
Concepts of Physics

12. If the tension in the

string in fgure (6-E3) is 16 N and
the accelerationof each block is 0-5 m/s, find the and the incline is L. Calculate the acceleration of the

coefficients at the two contacts with the

friction
blocks.
2-0kg block if (a) H, =020 and H, =030,(b) 4, =030
and 0-20. Take g= 10 m/s".

4,
4 ka
2kg
2kg
30 4 kg

30°

Figure 6-ES Figure 6-E6

13. The friction coeficient between the tableand the block 19. Two masses M, and M,are connected by a light rod
shown in figure (6-E4) is 02. Find the tensions in the
and the system is slipping down a rough incline of angle
two strings.
0 with the horizontal.The friction coefficient at both the
5 kg contacts is u. Find the acceleration of the system and
the force by the rod on one of the blocks.

20. A block of mass M is kept on a rough horizontal surface.

The coefficient of static friction between the block and

the surface is u. The block is to be pulled by applying

15 kg a force to it. What minimum force is needed to slide the
block ? In which direction should this force act ?
Figure 6-E4
21. The friction coeficient between the board and the floor
14. The shown in figure (6-E7) is u. Find the maximum force
friction coetficient between a road and the tyre of a that the man can exert on the rope so that the board
vehicle is 4/3. Find the maximum incline
the road may does not slip on the floor.
have so that once hard brakes are applied and the wheel
starts skidding, the vehicle going down at a speed of
36 knhr is stopped within 5 m.
15. The friction coefficient between an athelete's shoes and
the ground is 0-90. Suppose a superman wears these
shoes and races for 50m. There is no upper limit on his

capacity of running at high speeds. (a) Find the

minimum time that he will have to take in completing Figure 6-E7
the 50 m starting from rest. (b) Suppose he takes exactly
this minimum time to complete the 50m, what
minimum time will he take to stop ? 22. A 2 kg block is placed over a 4 kg block and both are
16. A car is going at a speed of 21-6 km/hr when it -placed on a smooth horizontal surface. The coefficient of
encounters a 12:8 m long slope ofangle 30° (figure 6-E5). friction between the blocks is 0-20. Find thè accleration
The friction coeffhicient between the road and the tyre is of the two blocks if a horizontal force of 12 N is applied
V2V3. Show that no matter how hard the driver applies to (a) the upper block, (b) the lower block. Take
the brakes, the car
greater than
will reach the bottom
36 km/hr. Take g= 10m/s
2

´oot
with a speed g=10 m/s

23. Find the accelerations a,, a,, a, of the three

shown in figure (6-E8) if a horizontal force of 10
blocks

N is

applied on (a) 2kg

2
block, (b) 3 kg block, (c) 7 kg block.
g
Take = 10 m/s

30° H=0.2
Hg*0.3
2kg
3 kg
Figure 6-E5 Hg0.0 7 kg

Figure 6-E8
17. A car starts from rest on a half kilometer long bridge.
The coefficient of friction between the tyre and the road
is 1:0. Show that one cannot drive
through the bridge 24. The friction
coefficient between the two blocks shown in
in less than 10 s. (6-E9) is u but the floor is smooth. (a). What
figure

contact sliding down maximum horizontal force F can be applied without

18. Figure (6-E6) shows two'blocks in
of 30°. The friction disturbing the equilibrium of the system ? (b) Suppose
an inclined surface inclination
the
between the block of mass 2-0 kg and the 'horizontal force applied is double of that found ir
ccefficient
the block of mass 4-0 kg part (a). Find the accelerations of the two masses.
incline is u,, and that between
 99

Friction

a rough vertical
m 2 kg is pushed against of static friction
29. A block of mass N, Coefficient
force of 40
wall with a force of 15 N,
is applied
M
being 05. Another horizontal
to the wall.
Will the
parallel
a direction find the
on the block in direction ? If no,
Pigure 6-E9 move ? If yes, in which
block wall on the block.
friutional force
exerted by the two
to be at rest between
(40 kg) is managing
95 Suppose the entire system of the previous question is 30. A person one wall A by his
hands and
walls by pressing
kept inside an elevator which is coming down with an vertical
feet and the other
wall B
by his back (figure 6-E11).
acceleration a <g. Repeat parts (a) and (b). coefficient between his body
oe Consider the situation shown in figure (6-E9). Suppose Assume that the friction friction acts
at all
and that limiting
a small electric field E exists in the space in the and the walls is 0-8 person pusl.3s the two
the
the contacts. (a) Show
that
upward direction and the upper block carries force exerted
vertically (b) Find the normal
The friction walls with equal force.
a posiive charge Q on its top surface. the person. Take g= 10 m/s.
coefficient between the two blocks is but the floor is by either wall on
emooth. What maximum horizontal force F can be
applied without disturbing the equilibrium ?
THint: The force on a charge Q by the electric field E
is F=QE in the direction of E.]

o7 A block of ass m slips on a rough horizontal table A

under the action of a horizontal force applied to it. The
coefficient riction between the block and the table is
of

u. The table does not move on the floor. Find the total
the
frictional. force applied by the floor on the legs of
table. Do you need the friction oefficient between the Figure 6-E11
table and the floor or the mass of the table ?

a small block of
mass m kept at
31. Figure (6-El2) shows mass M
and length l.
larger block of
the left end of a The system
on a horizontal road.
The system can slide an initial velocity v. The
towards right with
is started
and the bigger block
between the road
M m friction coefficient
block is W2. Find the time
is 4 and that
between the
from the
smaller blocks separates
elapsed before the
bigger block.

Figure 6-E10 m
M|

of the block of mass

in the M
28. Find the acceleration of friction
figure (6-E10). The
coefficient
of Figure 6-E12
situation
between the bigger
between the two blocks is u, and that

block and the ground is

ANSWERS
EXERCISES
I
OBJECTIVE 1. 0-4
6. (a)
4. (d) 5. (d) 2. 50 m
2. (b) 3. (c)
1. (b),
9. (d) 10. (a)
7. (c) 8. (b) 3. zero
4. 011
II
OBJECTIVE 5. 10 m
(d)
2. (b), (d)
3. (b), (c),
6. (a) 13 N (b) zero
1. (a), (b),(d)
5. (a), (b)
4. (c), (d)