Energy

Assertion is false but reason is true

Explanation

Assertion (A) is false because the power spent in doing a work depends inversely on time taken to do it so for a given amount of work performed at a faster rate i.e., in lesser time implies more power is spent.

Reason (R) is true because power depends inversely on the time taken to do a work so less time means more power spent, and vice versa.

Assertion is false but reason is true

Explanation

Assertion (A) is false because when the ball is released from a height, it falls down and the vertical height of the ball from the ground decreases. Therefore, the potential energy decreases and it changes to kinetic energy due to which the speed of ball increases.

Reason (R) is true because during the fall while transformation of mechanical energy from one form to the other desired form, some part of it changes to other undesirable form usually heat due to the presence of air resistance but when air resistance is absent then no losses occur and hence the total mechanical energy remains conserved.

(a) Work is said to be done by a force only when the body moves.

(b) Work done = Force x distance moved in the direction of force.

(c) The energy of a body is its capacity to do work.

(d) The S.I. unit of energy is joule .

(e) The potential energy of a body is due to its state of rest or position and kinetic energy of a body is due to its state of motion.

(f) Gravitational potential energy U = mass x force of gravity on unit mass x vertical height.

(g) Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ x mass x (speed)².

(h) Power P = Work done by the body / time taken.

(i) The S.I. unit of power is watt (W).

(j) 1 H.P. = 746 W.

The potential energy of a body at a certain height above the ground depends on the following factors:

1. The mass of the body — Greater the mass of the body, greater is the potential energy of the body.
2. Its height above the ground — More the height of the body above the ground, more is the potential energy.

Body B has greater potential energy.

Reason — Both bodies, A and B are at the same height above the ground. Value of g is also same for both. As the mass of body B (20 kg) is greater than that of body A (10 kg) hence potential energy of body B is greater.

(a) When a body of mass m is raised to height h above ground, a force is applied.

Force needed to lift the body (F) = weight of the body

If g is the force of gravity on mass of 1 kg, then the force of gravity on mass m kg will be mg N.

F = mg N

(b) Force = mg N; distance moved = h
Work done = force x distance moved = mg x h = mgh joule

(c) The work done against the force of gravity in lifting the body to a height h is stored in the body in form of its gravitational potential energy.

Potential energy (U) = mgh joule

Yes, a body can possess energy even when it is not in motion.

Example — A stone at rest placed at a height above the ground has potential energy. Water stored in a dam has potential energy.

Consider a ball placed at a height. It will have only potential energy and no kinetic energy.

If the ball is released from the height, it falls down and the vertical height of the ball from the ground decreases. Therefore, the potential energy decreases and it changes to kinetic energy due to which the speed of the ball increases. During the fall, the ball has both the potential energy and the kinetic energy. As the ball reaches the ground, the potential energy becomes zero and it changes entirely into kinetic energy.

The below figure shows the conversion of potential energy into kinetic energy during the vertical free fall of a ball at various positions A, B and C.

In a wound up watch spring the energy stored is potential energy. When the watch spring unwinds itself, the potential energy changes into kinetic energy and this kinetic energy is used to move the arms of the watch.

Given:
Force (F) = 30 N
Distance (d) = 5 m
Work done (W) = ?

Work done = Force x distance = 30 N x 5 m = 150 J

So, the work done by the force = 150 J.

Given:
Mass (m) = 20 kg
Distance (d) = Height = 2.5 m
Force of gravity on mass of 1 kg = 10 N
Work done (W) = ?

Force (F) = mg = 20 x 10 = 200 N

Work done = Force x distance = 200 x 2.5 = 500 J

So, the work done by the man = 500 J.

Given:
1 kgf = 10 N
10 kgf = 10 x 10 = 100 N
So, Force (F) = 100 N
Distance (d) = 0.5 m
Work done (W) = ?

Work done = Force x distance = 100 x 0.5 = 50 J

So, the work done by the force = 50 J.

Given:
Mass of first body = Mass of second body = m
Height of first body = h
Height of second body = 2h
g is same for both the bodies.

We know Gravitational potential energy = mgh

Gravitation potential energy of first body (U₁) = mgh
Gravitation potential energy of second body (U₂)= mg2h = 2mgh

On comparing both gravitational potential energy:

$\dfrac{\text{U}_1}{\text{U}_2} = \dfrac{\text{mgh}}{\text{2mgh}} = \dfrac{\text{1}}{\text{2}}$

So, gravitational potential energy of first body : gravitational potential energy of second body = 1 : 2.

Given:
Mass (m) = 2.5 kg
Height (h) = 15 m
Force of gravity on mass 1 kg = 10 N

Gravitational potential energy (U) = mgh = 2.5 x 10 x 15 = 375 J

So, gravitational potential energy = 375 J.

Given:
Gravitational potential energy (U) = 1.5 x 10⁴ J = 15000 J
Weight = 150 kgf = 150 x 10 = 1500 N
height h = ?

U = mgh

15000 = 1500 x h

h = $\dfrac{\text{15000}}{\text{1500}}$

h = 10 m

So height of the box = 10 m.

Given:
Potential energy (U) = 100 J
Mass (m) = 0.5 kg
Force of gravity on 1 kg mass = 10 N
height (h) = ?

U = mgh

100 = 0.5 x 10 x h

h = $\dfrac{\text{100}}{\text{5}}$

h = 20 m

So height of the tower = 20 m.

Given:
Mass (m) = 60 kg
Speed (v) = 50 m s^-1
Kinetic energy = ?

Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ x mv²

= $\dfrac{\text{1}}{\text{2}}$ x 60 x (50)²

= 30 x 2500

= 75000 J or 7.5 x 10⁴ J

So kinetic energy = 7.5 x 10⁴ J.

Given:

Mass (m) = 1000 kg

1 km h^-1 = $\dfrac{\text{5}}{\text{18}}$ m s^-1

36 km h^-1 = $\dfrac{\text{5}}{\text{18}}$ x 36 = 10 m s^-1

So, initial speed (v₁) = 10 m s^-1

1 km h^-1 = $\dfrac{\text{5}}{\text{18}}$ m s^-1

72 km h^-1 = $\dfrac{\text{5}}{\text{18}}$ x 72 = 20 m s^-1

So, final speed (v₂) = 72 km h^-1 = 20 m s^-1

Increase in its kinetic energy = ?

Increase in kinetic energy = $\dfrac{\text{1}}{\text{2}}$ m[(v₂)² - (v₁)²]

= $\dfrac{\text{1}}{\text{2}}$ x 1000 x [(20)² - (10)²]

= 500 x [400 - 100]

= 500 x 300

= 150000 J or 1.5 x 10⁵ J

So increase in kinetic energy = 1.5 x 10⁵ J.

Speed of first car = 15 km h^-1
Speed of second car = 30 km h^-1
Mass of both cars = m

Kinetic energy of first car (K₁) = $\dfrac{\text{1}}{\text{2}}$ x mv²

= $\dfrac{\text{1}}{\text{2}}$ x m x (15)²

= $\dfrac{\text{225}}{\text{2}}$ x m

= 112.5 m J

Kinetic energy of second car (K₂) = $\dfrac{\text{1}}{\text{2}}$ x mv²

= $\dfrac{\text{1}}{\text{2}}$ x m x (30)²

= $\dfrac{\text{900}}{\text{2}}$ x m

= 450 m J

Comparing the kinetic energy we get:

$\dfrac{\text{K}_1}{\text{K}_2} = \dfrac{\text{112.5 m}}{\text{450 m}} = \dfrac{\text{1}}{\text{4}}$

So Kinetic energy of first car (K₁) : Kinetic energy of second car (K₂) = 1 : 4.

Given:
Work done by pump = Energy spent = 4 x 10⁵ J or 400000 J
time = 10 s
Power = ?

Power = $\dfrac{\text{Work done}}{\text{time taken}}$

= $\dfrac{\text{400000}}{\text{10}}$

= 40000 W or 4 x 10⁴ W

So power spent by the pump = 4 x 10⁴ W.

(a) Both the girls move the same distance and force is also equal on both. Hence, the work done by both the girls is the same.
∴ Work done by girl A : Work done by girl B = 1 : 1

(b) Power spent = $\dfrac{\text{Work done}}{\text{time taken}}$

We know,

Work done by girl A = Work done by girl B = W

Power spent by girl A (P_A) = $\dfrac{\text{W}}{\text{20}}$

Power spent by girl B (P_B) = $\dfrac{\text{W}}{\text{15}}$

Comparing the power spent by girl A and girl B:

$\dfrac{\text{P} _\text{A}}{\text{P} _\text{B}} = \dfrac{\dfrac{\text{W}}{\text{20}}}{\dfrac{\text{W}}{\text{15}}} \\[1em] = \dfrac{\text{15}}{\text{20}} = \dfrac{\text{3}}{\text{4}}$

∴ Power spent by girl A : Power spent by girl B = 3:4.

joule

Reason — S.I. unit of work = S.I. unit of force x S.I. unit of distance = newton (N) x metre (m) or joule (J).

does not move

Reason — Work is said to be done if the force applied on the body makes the body move but if there is no motion in the body then work done is zero.

is more by coolie A than by B

Reason — Power spent = $\dfrac{\text{Work done}}{\text{time taken}}$.
Since coolie A takes less time than coolie B so power spent by coolie A is more than coolie B.

P = F x $\dfrac{\text{d}}{\text{t}}$

Reason — Power = $\dfrac{\text{Work done}}{\text{time taken}}$ and Work done = F x d
So P = F x $\dfrac{\text{d}}{\text{t}}$.

746 W

Reason — 1 H.P. = 746 W.

four times

Reason — Kinetic energy = $\dfrac{\text{1}}{\text{2}}$ mv²
If speed gets doubled then kinetic energy becomes four times.

double

Reason — Potential energy (P.E.) is given by expression mgh.

In first case P.E. = mg x 2 or 2mg [h = 2 m]
In second case P.E. = mg x 4 or 4mg [h = 4 m]

So potential energy gets doubled.

kinetic, potential

Reason — Whenever mechanical energy changes to other forms, it is always in the form of kinetic energy and not in the form of potential energy i.e., the stored potential energy first changes to kinetic energy and then kinetic energy changes to the other forms.

3.6 x 10⁶ J

Reason — As,

1 kilo (k) = 1000
1 hour (h) = 3600 seconds (s)

1 kWh = 1 x 1000 Wh
= 1 x 1000 x 3600 Ws
= 3600000 J
= 3.6 x 10⁶ J

Where,

1 J = 1 Ws

The work done by a force on a body is equal to the product of the force applied and the distance moved by the body in the direction of force i.e.,

Work done = Force x distance moved in the direction of force

A force performs work when it changes the position of the body or it changes the size or shape of the body.

The two conditions where no work is done by a force are:

1. If the force applied on a body does not move the body i.e. displacement is zero.
2. If the displacement produced by applied force is normal to the direction of force.

Work is done in the following two cases:

(b) A boy climbing up the stairs: Work is done by the boy as the boy changes his position.

(d) A girl moving on the road: Work is done as displacement is produced by the body.

Work done = Force x distance moved in the direction of force
W = F x d

The S.I. unit of work is joule (J). One joule of work is said to be done if one newton force when acting on a body moves it by 1 metre in the direction of force.

The two factors on which the work done on a body depends are:

1. The magnitude of the force applied.
2. The distance moved by the body in the direction of force.

The energy of a body is its capacity to do work. The energy of a body in a state is equal to the work done on the body to bring it to that state.

The S.I. unit of energy is joule(J).

A body is said to possess an energy of 1 joule if it can do one joule work or if one joule work is done on it.

There is a direct relationship between work and energy. To do more amount of work we need to spend more energy. Similarly, the work done on a body in changing its state is said to be the energy possessed by the body.

The two kinds of mechanical energy are:

1. Potential energy
2. Kinetic energy

Potential energy of a body is the energy possessed by it due to its state of rest or position. Its unit is joule (J).

(a) A stone placed at a height has potential energy because of its position. It is known as gravitational potential energy.

(b) A stretched rubber band has potential energy due to its elongated stretched state. It is known as elastic potential energy.

The bucket kept on second floor has greater potential energy.

Reason — The two buckets are identical containing the same amount of water so their mass is same. Value of g is also same for the two buckets. As the bucket on second floor is at a greater height hence its potential energy is also greater.

Gravitational potential energy (U) = mgh

where,
m is mass of the body,
g is acceleration due to gravity and
h is height of the body above ground level.

Kinetic energy of a body is the energy possessed by it due to its state of motion. Example: A fast moving stone has kinetic energy which has the capacity of breaking a window pane.

The two factors on which the kinetic energy of a moving body depends are:

1. The mass of the body — Greater the mass of the body, higher is its kinetic energy.
2. The speed of the body — More the speed of the body, higher is its kinetic energy.

The toy car B has greater kinetic energy than toy car A.

Reason — The two toy cars A and B are moving with the same speed. As the toy car B has greater mass (500 g) than toy car A (200 g) hence its kinetic energy is also greater.

Kinetic energy of cyclist will increase as speed is doubled because more the speed of the body, more is its kinetic energy.

The expression for the kinetic energy of a body (K.E.) = $\dfrac{\text{1}}{\text{2}}$ mv²
Where, m is mass of the body and
v is speed of the body.

Kinetic energy of ball (K.E.) = $\dfrac{\text{1}}{\text{2}}$ mv²
Where,
m is mass of the ball and
v is speed of the ball.

Potential Energy.

(a) A moving cricket ball has kinetic energy due to its state of motion.

(b) A stone at rest on the top of a building has potential energy due to its raised position.

(c) A compressed spring has potential energy due to its compressed state.

(d) A moving bus has kinetic energy due to its state of motion.

(e) A bullet fired from a gun has kinetic energy due to its state of motion.

(f) Water flowing in a river has kinetic energy due to its state of motion.

(g) A stretched rubber band has potential energy because of its stretched position.

(a) When an electric bulb glows, the electrical energy changes into heat and light energy.

(b) In electric oven, electrical energy changes into heat energy .

(c) In loudspeaker, electrical energy is converted into sound energy.

(d) A microphone converts sound energy into electrical energy.

(e) An electric motor converts electrical energy into mechanical energy.

(f) A wind mill converts mechanical energy into electrical energy.

A coolie with a luggage on his head and moving on a road does no work against force of gravity as the direction of motion of the coolie is perpendicular to the direction of force of gravity.

Work done by the moon is zero as the force of attraction on moon by earth is normal to the direction of motion of moon.

Work is said to be done only when there is change in position or size and shape of the body. When a man pushes the wall it does not move so no work is done.

When a hammer is lifted it has potential energy due to its raised position and then when it is struck it drives the nail into the wood due to its potential energy.

A horse has more kinetic energy than a dog. Kinetic energy of a body depends on mass and speed of the body. Since both dog and horse have same speed but mass of horse is more than that of dog so horse has more kinetic energy than a dog.

As the teacher moves around in the class, he/she is in a state of motion, there is change in his/her position due to application of force. Hence, work is done by the teacher.
On the other hand, a child standing and reading a book is stationary. There is no change in his/her position. Hence, no work is done by the child.

Kinetic energy.

No. In real life we can’t convert one form of energy completely into another useful form. Some energy is always lost (dissipated) to the surroundings as heat, sound, vibration, friction, etc., so efficiency is always less than 100%. For example, an electric bulb gives light but also produces heat; a car engine changes fuel energy into motion but lots becomes heat and sound. Total energy is conserved, but not all of it stays in a form we can use.

When I stand still on the escalator, I’m not applying an upward force through the 30 m height, so the work done by me is 0 J (approximately zero). The escalator’s motor provides the upward force and does the work equal to mgh to lift me to level 4. (If I had climbed myself, then I would have done mgh work.)

(a) True

(b) False
Correct Statement — The energy stored in water of a dam is potential energy.

(c) True

(d) False
Correct Statement — Work done by a boy depends on the magnitude of force applied and distance moved by the body in the direction of force.

(e) True