Work and Energy

Question (1) Look at the activities listed below. Reason out whether or not work is done in the light of your understanding of the term 'work'.

(a) Suma is swimming in a pond

(b) A donkey is carrying a load on its back.

(c) A wind-mill is lifting water from a well.

(d) A green plant is carrying out photosynthesis.

(e) An engine is pulling a train.

(f) Food grains are getting dried in the sun.

(g) A sailboat is moving due to wind energy.

Answer

We know that, Work done (W) = Force (F) × Displacement (s)

This means, work to be done, there are two conditions must be satisfied. First Force should be applied to the object and second displacement should be done. Since, work done is the product of force (F) and displacement (s), thus, in the case of any one would be zero, the work done would be equal to zero.

(a) Suma is swimming in a pond

Answer:

In the course of swimming, force is applied on the water, and displacement takes place. Thus, work is done.

So, work done in the case Suma is swimming in a pond.

(b) A donkey is carrying a load on its back.

Answer:

In this case two case can be assumed.

(i) If the donkey only stand still after keeping the load on its back, then here displacement is equal to zero. And thus no work is done.

(ii) If the donkey is walking or going with load on his back, then while walking, force is applied and displacement takes place. Thus, in this case work is done.

(c) A wind-mill is lifting water from a well.

Answer: Here work is done. Because force is applied to the water, and water is displaced.

(d) A green plant is carrying out photosynthesis.

Answer:Here since no displacement is done, thus no work is done.

(e) An engine is pulling a train.

Answer:Since, displacement takes place while applying the force by engine to the train, thus, work is done.

(f) Food grains are getting dried in the sun.

Answer: Here, no force and no displacement takes place. Thus, work is not done.

(g) A sailboat is moving due to wind energy.

Answer:Here force is applied by wind energy on the boat and boat is displaced because of that force. Thus, work is done.

Question (2) An object thrown at a certain angle to the ground moves in a curved path and falls back to the ground. The initial and the final points of the path of the object lie on the same horizontal line. What is the work done by the force of gravity on the object?

Answer: Work done because of gravity depends upon the vertical displacement.

Here vertical displacement, i.e. h = 0

We know that, work done (W) = mgh

Since, here, h =0, thus, Work done = mg × 0 = 0

Thus, in the given condition, work done by the force of gravity on the object is equal to zero.

Question (3) A battery lights a bulb. Describe the energy changes involved in the process.

Answer:

When a battery lights a bulb, the chemical energy of the battery is changed into to electrical energy. Electric energy passes to the bulb is changed into light energy and heat energy.

Chemical Energy → Electric Energy → Light energy + Heat energy.

Question (4) Certain force acting on a 20 kg mass changes its velocity from 5 m s^–1 to 2 m s^–1. Calculate the work done by the force.

Answer:

Given, m = 20 kg

Initial velocity (u) = 5 m/s

Final velocity (v) = 2 m/s

Thus, Work done =?

We know that, work done = change in kinetic energy.

We know that, change in kinetic energy,

= 10 × (4 – 25) J

= 10 × (– 21) J

= – 210 J

Thus, work done = Change in Kinetic energy = – 210 J Answer

Question ( 5) A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force? Explain your answer.

Answer:

Here, work done is equal to zero. Because work done due to gravitational force depends upon the height. Here, height is equal to zero and hence work done is equal to zero.

Given, m = 10 kg

Height, h = 0

We know that, work done on the object by the gravitational force, W = mgh

⇒ W = 10 kg × g × 0

⇒ W = 0

Thus, work done = 0

Question (6) The potential energy of a freely falling object decreases progressively. Does this violate the law of conservation of energy? Why?

Answer: No. This does not violate the law of conservation of energy. Because

During free fall of an object; the potential energy of the object decreases progressively. And at any point in its path, an equal amount of increase in kinetic energy. And thus there is a continual transformation of gravitational potential energy into kinetic energy.

But at every point, the sum of potential energy and kinetic energy is constant.

Question (7) What are the various energy transformations that occur when you are riding a bicycle?

Answer: In the course of riding a bicycle first of all while pedaling, the muscular energy is transferred into kinetic energy and heat energy.

This kinetic energy of motion of the legs is transferred into kinetic energy of pedal and finally cycle is set to be moved.

Muscular energy → Kinetic energy + Heat Energy ⇒ Kinetic Energy

Question (8) Does the transfer of energy take place when you push a huge rock with all your might and fail to move it? Where is the energy you spend going?

Answer:

No energy is transfer to the rock when a person push a huge rock with all his might and fail to move. Here because displacement is zero hence work done is equal to zero.

In this case muscular energy is transferred into heat energy.

Question (9) A certain household has consumed 250 units of energy during a month. How much energy is this in joules?

Answer:

We know that, 1 unit of energy = 1 kWh

And, 1 kWh = 3.6 x 10⁶ J

Thus, 250 kWh = 250 x 3.6 x 10⁶ J

= 9 x 10⁸ J Answer

Question (10) An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Answer:

Here given mass (m) = 40 kg

Height (h) = 5 m

Now, we know that, Potential Energy = mgh

= 40 kg x 9.8 ms^–2 x 5 m

Thus, potential energy = 1960 J

At halfway down, i.e. at the height of 2.5 m

Potential energy = 1960 J/2 = 980 J

Since according to Law of Conservation of energy, the total energy is fixed.

Thus, at halfway down, Kinetic Energy = Potential Energy

Hence, Kinetic Energy at halfway down = 980 J Answer

Question (11) What is the work done by the force of gravity on a satellite moving round the earth? Justify your answer.

Answer:

We know that, if displacement of object and force applied is perpendicular to each other, then work done is zero.

Here, the movement of the satellite and force applied by the gravity is perpendicular to each other, thus, work done by the force of gravity on satellite is equal to zero.

Question (12) Can there be displacement of an object in the absence of any force acting on it? Think. Discuss this question with your friends and teacher.

Answer:We know that, in the case of uniform motion, no external force is acting on the object.

Thus, when object is in uniform motion there is displacement on an object in the absence of any force acting on the object.

Question (13) A person holds a bundle of hay over his head for 30 minutes and gets tired. Has he done some work or not? Justify your answer.

Answer:

We know that, work done (W) = Force (F) × Displacement (s)

When a person holds a bundle of hay or anything over his head for any time, there is no displacement takes place. This means displacement is equal to zero. And hence, work done will be zero.

Thus, in the given condition, work done = 0 Answer

Question (14) An electric heater is rated 1500 W. How much energy does it use in 10 hours?

Answer:

Given, Power (P) = 1500 W

Time (t) = 10 h

Thus, energy consumed = ?

We know that, energy consumed = P × t

Therefore, Energy consumed = 1500 W x 10 h

= 15000 W h

Or, Energy consumed = 15 kWh Answer

Question (15) Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?

Answer:

We know that according to Law of Conservation of Energy, energy neither be created nor be destroyed. But only the form of energy can be changed.

The law of conservation of energy can be observed in the case of pendulum.

Let a simple pendulum is given in the figure.

In the simple pendulum, A and B are it extreme left and right positions while O is the mean position.

When the pendulum is stretched to its extreme left position A, it reaches to its maximum height. Here potential energy of the pendulum is maximum while kinetic energy is zero.

After set the pendulum free from the position A, it gradually reaches to its mean position O. At this mean position the kinetic energy becomes maximum while potential energy becomes zero.

From the mean position pendulum reaches to its extreme right position, B. At position B again the kinetic energy becomes zero while the potential energy is maximum.

However in all the three positions, A, O and B, the sum of kinetic energy and potential energy remains constant. And hence, the pendulum obeys the Law of Conservation of Energy.

Now, according to Law of conservation of energy, pendulum should never be stopped. But because of resistance of air, some of the energy is utilized gradually to overcome the resistance and changed into heat. Gradually all of the energy of pendulum goes to surrounding and changes into heat and other energy. And finally pendulum stops. But in all the situations the total energy of the system remains constant.

Thus, a pendulum does not violate the Law of Conservation of Energy.

Question (16) An object of mass, m is moving with a constant velocity, v. How much work should be done on the object in order to bring the object to rest?

Answer:

Given; mass = m and velocity = v

Thus, as we know that, kinetic energy = ½ mv²

Now, to come in rest kinetic energy should be zero. Thus work done is equal to the kinetic energy of the object.

Thus, wor done = kinetic energy = ½ mv² Answer

Question (17) Calculate the work required to be done to stop a car of 1500 kg moving at a velocity of 60 km/h?

Answer:

Given, mass of car (m) = 1500 kg

Velocity of car (v) = 60 km/h

Or, v = 16.66 m/s

Then, work done to stop the car =?

We know that work done = kinetic energy of the car

And we know that, kinetic energy = ½ mv²< /p>

= ½ 1500 x 16.67²< /p>

= 208333.33 J

= 20.8 x 10⁴ J

work required to be done to stop a car = 20.8 x 10⁴ J Answer

Question (18) In each of the following a force, F is acting on an object of mass, m. The direction of displacement is from west to east shown by the longer arrow. Observe the diagrams carefully and state whether the work done by the force is negative, positive or zero.

Answer:

We know that, (a) If the direction of force is perpendicular to the direction of displacement, then work done is equal to zero>

(b) If the direction of force is the same as direction of displacement then, work done is positive.

(c) If the direction of force is opposite of the displacement, then work done is negative.

Thus,

In first figure, since the direction of force is perpendicular to displacement, hence work done is zero.

In the second figure, since the direction of force and direction of displacement are same, thus work done is positive.

In the third figure, since the directions of force and displacement are opposite, thus work done is negative.

Question (19) Soni says that the acceleration in an object could be zero even when several forces are acting on it. Do you agree with her? Why?

Answer:

Yes, I agree with Soni.

Because, in the case of uniform motion, acceleration is zero while several forces acting on an object cancel out each other.

Question (20) Find the energy in kW h consumed in 10 hours by four devices of power 500 W each.

Answer:

Given; Power (P) = 500 W

Time (t) = 10 h

And, number of devices = 4

Thus, energy consumed =?

We know that, Energy consumed = Power(P) x Time (t)

Thus, energy consumed by one given device = 500 W × 10 h

= 5000 W h

= 5 kWh

Thus, energy consumed by 4 devices = energy consumed by one device × 4

= 5 kWh × 4 = 20 kWh

Thus, total power consumed = 20 kWh Answer

Question (21) A freely falling object eventually stops on reaching the ground. What happens to its kinetic energy?

Answer:

Just before hitting the ground by a free falling object, the potential energy of the object becomes zero and kinetic energy becomes maximum. After stops on reaching the ground, the kinetic energy changes into heat energy and sound energy.