Given in Fig. 5.11 are examples of some
potential energy functions in one
dimension. The total energy of the
particle is indicated by a cross on the
ordinate axis. In each case, specify the
regions, if any, in which the particle
cannot be found for the given energy.
Also, indicate the minimum total
energy the particle must have in each
case. Think of simple physical contexts
for which these potential energy shapes
are relevant.
A body of mass 2 kg initially at rest
moves under the action of an applied
horizontal force of 7 N on a table with
coefficient of kinetic friction = 0.1.
Compute the
(a) work done by the applied force in
10 s,
(b) work done by friction in 10 s,
(c) work done by the net force on the
body in 10 s,
(d) change in kinetic energy of the
body in 10 s,
and interpret your results.
The sign of work done by a force on a body is important to understand. State carefully
if the following quantities are positive or negative:
(a) work done by a man in lifting a bucket out of a well by means of a rope tied to the
bucket.
(b) work done by gravitational force in the above case,
(c) work done by friction on a body
sliding down an inclined plane,
(d) work done by an applied force on
a body moving on a rough
horizontal plane with uniform
velocity,
(e) work done by the resistive force of
air on a vibrating pendulum in
bringing it to rest.
See Fig. 4.15. A wooden
block of mass 2 kg rests on a soft horizontal
floor. When an iron cylinder of mass 25 kg
is placed on top of the block, the floor yields
steadily and the block and the cylinder
together go down with an acceleration of
0.1 m s
–2. What is the action of the block
on the floor (a) before and (b) after the floor
yields ? Take g = 10 m s–2. Identify the
action-reaction pairs in the problem.
A circular racetrack of
radius 300 m is banked at an angle of 15°.
If the coefficient of friction between the
wheels of a race-car and the road is 0.2,
what is the (a) optimum speed of the race-
car to avoid wear and tear on its tyres, and
(b) maximum permissible speed to avoid
slipping ?
A cyclist speeding at
18 km/h on a level road takes a sharp
circular turn of radius 3 m without reducing
the speed. The co-efficient of static friction
between the tyres and the road is 0.1. Will
the cyclist slip while taking the turn?
What is the acceleration of
the block and trolley system shown in a
Fig. 4.12(a), if the coefficient of kinetic friction
between the trolley and the surface is 0.04?
What is the tension in the string? (Take g =
10 m s-2). Neglect the mass of the string.
See Fig. 4.11. A mass of 4 kg
rests on a horizontal plane. The plane is
gradually inclined until at an angle θ = 15°
with the horizontal, the mass just begins to
slide. What is the coefficient of static friction
between the block and the surface ?
Determine the maximum
acceleration of the train in which a box
lying on its floor will remain stationary,
given that the co-efficient of static friction
between the box and the train’s floor is
0.15.
See Fig. 4.8. A mass of 6 kg
is suspended by a rope of length 2 m
from the ceiling. A force of 50 N in the
horizontal direction is applied at the mid-
point P of the rope, as shown. What is the
angle the rope makes with the vertical in
equilibrium ? (Take g = 10 m s-2). Neglect
the mass of the rope.
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