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The work done on a body moving in a circular path is zero. Justify.

The work done on a body moving in a circular path is also zero. This is because, when a body moves in a circular path, then the centripetal force acts along the radius of the circle, and it is at right angles to the motion of the body. Thus, the work done in the case of moon moving round the earth is also zero. From this discussion it is clear that it is possible that a force is acting on a body but still the work done is zero.


Calculate the kinetic energy of a body of mass 2kg moving with a velocity of 0.1 metre per second.

The formula for calculation kinetic energy is:

Kinetic energy = mv2

Here, Mass, m = 2 kg

And, Velocity, v = 0.1m/s

So, putting these values in the above formula, we get:
Kinetic energy = x 2 x (0.1)2
= x 2 x 0.1 x 0.1
                     = 0.01J
Thus, the kinetic energy of the body is 0.01joule.


When the speed of a moving object is doubled, what happens to its kinetic energy?

When the speed of a moving object is doubled, its kinetic energy is increased four times.


Which would have a greater effect on the kinetic energy of an object, doubling the mass or doubling the velocity?

(i) The kinetic energy of a body is directly proportional to its ‘mass’ (m). So, if we double the mass (so that it becomes 2m), then the kinetic energy will also get doubled.

(ii) On the other hand, kinetic energy of a body is directly proportional to the "square of its velocity"(v2). So, if we double the velocity (so that it becomes 2v), then the kinetic energy will become four times. This is because:(2 v)2 =4v2.

It is clear from the above discussion that doubling the velocity has a greater effect on the kinetic energy of an object.


If acceleration due to gravity is 10m/s2, what will be the potential energy of a body of mass 1kg kept at a height of 5m?

The potential energy of a body is calculated by using the formula:
Potential Energy = m x g x h
Mass, m = 1kg
Acceleration due to gravity, g = 10m/s2
Height, h = 5m
So, putting these values in the above formula, we get:
Potential Energy = 1 x 10 x 5 = 50J
Thus, the potential energy of the body is 50 joules.


How much work is done by a force of 10N in moving an object through a distance of 1m in the direction of the force?

The work done is calculated by using the formula:
W = F x S
Hence, Force, F = 10N
And, Distance, S = 1m
So, Work done, W = 10 x 1J  = 10J
Thus the work done is 10 Joules.


Note on transformation of sun’s energy into wind energy.

The sun’s heat causes uneven heating of land and produces different air pressures at different places. These different air pressures produce wind having kinetic energy. In this way, the sun’s energy is transformed into kinetic energy (of wind). In other words, the sun supplies us the energy of wind. We use this wind energy for many purposes.


Define escape velocity.

The minimum velocity which an object (like a rocket) should have in order to overcome the earth’s gravity and enter into space is called escape velocity. The escape velocity for all the objects from the earth has been found to be 11.10kilometres per second (11.16km/s).


Compare the vertical and horizontal component of velocity of a projectile.

The horizontal velocity u cos of the object remains constant through out the flight of the object. The vertical velocity of the object changes with uniform acceleration (which is the acceleration due to gravity).


Write a note on "satellite as a projectile" which is in orbit around the earth.

A satellite remains in orbit outside the earth’s atmosphere where the friction is very small. Thus, it can be thought of as a projectile. It must be accelerating towards the earth under the action of gravity, because its direction changes all the time. It is very important to note here that, it is the gravitational attraction of the sun which keeps the planets revolving round it in their orbits, and it is the gravitational attraction of the earth which makes the moon(or artificial satellite) go round the earth repeatedly.


What did primitive men use as a source of energy?

Primitive men made use of fire as an external source of energy for heating, lighting and cooking. He then learnt to harness natural energy to fulfill his needs. The energy of the wind was the first to be harnessed. During the Middle Ages windmills were used extensively for grinding grain. The energy of falling water was harnessed by the use of waterwheels and turbines. Now he generates energy from natural sources such as Sun, water and fuels through efficient and advanced techniques. He has devised combustion engines, thermoelectric, hydroelectric and nuclear power plants as powerful and efficient means of generating energy.


A man carrying a bucket of water is walking on a level road with a uniform velocity. Does he do any work on the bucket while carrying it?

Since the velocity is uniform, the man exerts no net force on the bucket in the horizontal direction, i.e., the direction in which he carries the bucket. The only force he exerts on the bucket is against gravity and this force is perpendicular to the direction of motion, i.e. the angle q between the force and displacement is 90. Therefore work done is W = FS cos q = FS cos 90° = 0.


When is the work done by a force positive and when is it negative?

When a force acts on a body in the direction of motion, the work done by the force is taken to be positive. But if the force acts in a direction opposite to the direction of motion, the work done by the force is taken to be negative.


With an example derive the equation for kinetic energy of a moving body.

Let us consider a trolley which is initially at rest on a horizontal, smooth surface having negligibly small friction such as that of ice. If the trolley is pushed with a constant horizontal force, it begins to move. But if the force is withdrawn, the trolley still continues to move with a uniform velocity v. The trolley is set into motion by the initial work done on it to move from rest. When we push the trolley with a constant force, it gets accelerated. Suppose it moves a distance s in the time interval t. Thus
W = Fs ----(1)
By, Newton’s second law of motion
F = ma ----(2)
m being the mass of the trolley. The distance s moved by the trolley through the acceleration, a, during the time t is given by
s = ut + at2 ----(3)
Further, the velocity v it attains after time t is given by
v = u + at ----(4)
Since the trolley has started from rest, u = 0 in equations (3) and (4). The velocity v is thus the velocity, which the trolley attains when the force F is withdrawn.
Substituting equation (2) for F and equation (3) for s in equation (1), we get
W = ma
× at2
    = m (at)2
    = mv2 [from equation (4)]
The work done is stored in the form of kinetic energy of the body.


A car is moving with a uniform velocity of 45 km/h. What is the kinetic energy of an object of mass 35 kg kept in the car?

We know that both the object and the car is moving with the same velocity, i.e.,

v = 45 km/h = = 12.5 m/s2

Mass of the object m = 35 kg

Kinetic energy possessed by the object

K.E. = mv2

× 35 kg × (12.5 m/s2)2

      = 2734.38 J.


Explain briefly elastic potential energy with an example?

Potential energy can also be stored due to change in the shape of an object. For example, when we stretch a rubber band or a spring, the stretched spring and the rubber band possess potential energy. This energy is called elastic potential energy.


A crane lifts a car upto a certain height in 1 minute. A second crane lifts the same car upto the same height in 2 minutes. Which crane supplies the greater power? Which crane consumes more fuel?

The two cranes do the same amount of work, i.e.,
W = mass of the car
× acceleration due to gravity × height of the lifted car.
Hence both cranes consume the same amount of fuel. The first crane does the same amount of
work in half the time than the second crane. Hence the first crane supplies two times more power than the second crane.


With an example explain the transformation of energy.

When we throw a ball, we transform the energy stored in our body into kinetic energy of the ball. When we lift the ball from the ground, we transform this energy into potential energy. If this ball is released from a height above the earth, the earth pulls it down, does work on it and the gravitational potential energy is transformed into kinetic energy. When the ball strikes the ground, the stored kinetic energy gets transformed into sound energy.


Explain the energy transformation of sun’s radiation.

The sun’s heat energy is the result of atomic and chemical energy changes in its interior and on its surface respectively. A part of the energy of radiation from the sun, travelling through space with the velocity of 3 ´ 108 m/s, is used up in heating the dry land and the air which in turn causes winds and storms. A part of energy is also used to heat and evaporate water vapour from the oceans. Most of this energy is utilized when water condenses to clouds, which produce rains. At high altitudes, snow is deposited and this mass of water has huge potential energy. On its way to the sea, this potential energy of the water gets converted into kinetic energy and can thus be transformed into electrical energy at hydroelectric plants.


An artificial satellite orbiting the earth at an altitude of a few hundred kilometers loses a small amount of energy as heat due to friction of the thin atmosphere at that altitude. Why then does its speed increase progressively as it comes closer and closer to the earth?

As a satellite comes closer to the earth, its potential energy decreases. According to the law of conservation of energy, the total energy of the system must remain constant.
Now, total energy = KE + PE + heat energy

Since the heat loss is very small, a decrease in potential energy results in a net increase in kinetic energy. Hence the speed of a satellite progressively increases as it comes closer and
closer to the earth.

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