A molecule in a gas container hits a horizontal wall with speed 200 m s–1 and angle 30°
with the normal, and rebounds with the same speed. Is momentum conserved in the
collision ? Is the collision elastic or inelastic ?
A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with
decreasing acceleration (due to viscous resistance of the air) until at half its original
height, it attains its maximum (terminal) speed, and moves with uniform speed
thereafter. What is the work done by the gravitational force on the drop in the first
and second half of its journey ? What is the work done by the resistive force in the
entire journey if its speed on reaching the ground is 10 m s–1 ?
An electron and a proton are detected in a cosmic ray experiment, the first with kinetic
energy 10 keV, and the second with 100 keV. Which is faster, the electron or the
proton ? Obtain the ratio of their speeds. (electron mass = 9.11×10-31 kg, proton mass
= 1.67×10–27 kg, 1 eV = 1.60 ×10–19 J).
A body constrained to move along the z-axis of a coordinate system is subject to a
constant force F given by
ˆ
2
ˆ ++−= 3
ˆ
kjiF N
where k ,j ,i
ˆ ˆ ˆ are unit vectors along the x-, y- and z-axis of the system respectively.
What is the work done by this force in moving the body a distance of 4 m along the
z-axis ?
A body is moving unidirectionally under the influence of a source of constant power.
Its displacement in time t is proportional to
(i) t
1/2 (ii) t (iii) t
3/2 (iv) t
2
Answer carefully, with reasons :
(a) In an elastic collision of two billiard balls, is the total kinetic energy conserved
during the short time of collision of the balls (i.e. when they are in contact) ?
(b) Is the total linear momentum conserved during the short time of an elastic collision
of two balls ?
(c) What are the answers to (a) and (b) for an inelastic collision ?
(d) If the potential energy of two billiard balls depends only on the separation distance
between their centres, is the collision elastic or inelastic ? (Note, we are talking
here of potential energy corresponding to the force during collision, not gravitational
potential energy).
State if each of the following statements is true or false. Give reasons for your answer.
(a) In an elastic collision of two bodies, the momentum and energy of each body is
conserved.
(b) Total energy of a system is always conserved, no matter what internal and external
forces on the body are present.
(c) Work done in the motion of a body over a closed loop is zero for every force in
nature.
(d) In an inelastic collision, the final kinetic energy is always less than the initial
kinetic energy of the system.
Underline the correct alternative :
(a) When a conservative force does positive work on a body, the potential energy of
the body increases/decreases/remains unaltered.
(b) Work done by a body against friction always results in a loss of its kinetic/potential
energy.
(c) The rate of change of total momentum of a many-particle system is proportional
to the external force/sum of the internal forces on the system.
(d) In an inelastic collision of two bodies, the quantities which do not change after
the collision are the total kinetic energy/total linear momentum/total energy of
the system of two bodies.
Answer the following :
(a) The casing of a rocket in flight
burns up due to friction. At
whose expense is the heat
energy required for burning
obtained? The rocket or the
atmosphere?
(b) Comets move around the sun
in highly elliptical orbits. The
gravitational force on the
comet due to the sun is not
normal to the comet’s velocity
in general. Yet the work done by the gravitational force over every complete orbit
of the comet is zero. Why ?
(c) An artificial satellite orbiting the earth in very thin atmosphere loses its energy
gradually due to dissipation against atmospheric resistance, however small. Why
then does its speed increase progressively as it comes closer and closer to the earth ?
(d) In Fig. 5.13(i) the man walks 2 m carrying a mass of 15 kg on his hands. In Fig.
5.13(ii), he walks the same distance pulling the rope behind him. The rope goes
over a pulley, and a mass of 15 kg hangs at its other end. In which case is the work
done greater ?
The potential energy function for a
particle executing linear simple
harmonic motion is given by V(x) =
kx2/2, where k is the force constant
of the oscillator. For k = 0.5 N m-1
,
the graph of V(x) versus x is shown
in Fig. 5.12. Show that a particle of
total energy 1 J moving under this
potential must ‘turn back’ when it
reaches x = ± 2 m.
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