Work Energy and Simple Machines Class 9 Notes Science Chapter 7 - #NCSOLVE 📚

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Class 9 Science Chapter 7 Work Energy and Simple Machines Notes

Class 9 Science Exploration Chapter 7 Notes

Class 9 Science Chapter 7 Notes – Class 9 Work Energy and Simple Machines

→ Work: Work is said to be done when a force applied on an object produces displacement in the direction of the force.

If a constant force F causes displacement s, then work done W = F × s.
More precisely, W = Fs cosθ, where θ is the angle between force and displacement.
Work is maximum when force and displacement are in the same direction (θ = 0°) and zero when perpendicular (θ = 90°).
Work depends on the effect of force over a distance, not just force alone.

→ SI Unit of Work: The SI unit of work is joule (J). is named after the scientist James Prescott Joule. He studied how mechanical energy and thermal energy are related, and can be converted from one to the other. This helped develop a unified way to understand energy. One joule is defined as the work done when a force of 1 newton moves an object through a distance of 1 metre in the direction of the force. 1 J = 1 N m.

→ Work is a scalar quantity, meaning it has only magnitude and no direction, even though force and displacement are vectors.

→ Zero Work: Work done is zero in three situations. First, when no force is applied (F = 0), so nothing can cause energy transfer. Second, when there is no displacement (s = 0), even if a large force is applied, such as pushing a wall that does not move.

→ Third, when force is perpendicular to displacement, such as centripetal force in circular motion, where force changes direction but does not contribute to motion in that direction.

→ Positive Work: Work and displacement are in the same direction ( θ between 0° and 90°). In this case, force helps motion and increases the object’s energy.

Examples include pushing a cart or wheelchair forward or gravity acting on a falling object. Positive work generally increases kinetic energy.

→ Negative Work: Work is negative when force acts opposite to displacement (θ between 90° and 180°). In this case, force opposes motion and removes energy from the system. Examples include friction slowing down a moving object or a goalkeeper stopping a moving ball. Negative work reduces kinetic energy.

→ Work-Energy Theorem: The work-energy theorem states that the net work done on an object equals the change in its kinetic energy.
W_net = ∆K = K_final – K_initial. This means work is net final internal directly responsible for changing motion. If
positive work is done, kinetic energy increases; if negative work is done, kinetic energy decreases.

→ Energy: Energy is the capacity to do work. It is the ability of a system or object to cause change, especially to apply force and produce motion. Energy exists in many forms such as mechanical, heat, light, chemical, and electrical. The SI unit of energy is joule, same as work. Energy is also a scalar quantity and cannot be created or destroyed, only transformed.

→ Kinetic Energy (K): Kinetic energy is the energy possessed by a body due to its motion. It depends on mass and velocity. The formula is K =\(\frac{1}{2}\) mv².

→ This shows that kinetic energy increases with the square of speed, so doubling speed increases kinetic energy four times. Faster and heavier objects have more kinetic energy.

→ Potential Energy (U): Potential energy is stored energy due to position or configuration. Gravitational potential energy is U = mgh, where m is mass, g is acceleration due to gravity, and h is height above reference level. It represents energy stored due to height. Other forms include elastic potential energy stored in stretched or compressed objects like springs.

→ Mechanical Energy: Mechanical energy is the sum of kinetic energy and potential energy of an object. M.E. = K.E. + P.E. It represents total energy due to motion and position. In ideal conditions without non-conservative forces like friction, mechanical energy remains constant.

→ Gravitational Potential Energy: It is the energy possessed by an object due to its position above the surface of the Earth. It is equal to the work done in lifting the object against the force of gravity.

→ Conservation of Mechanical Energy: The law of conservation of mechanical energy states that when only conservative forces (like gravity) act, total mechanical energy remains constant. As an object falls, potential energy decreases while kinetic energy increases by the same amount.

→ However, in real life, friction and air resistance convert some mechanical energy into heat, so total mechanical energy is not strictly conserved.

→ Power (P): Power is the rate of doing work or rate of energy transfer. It is given by P= W/t. A higher power means more work is done in less time. The SI unit is watt (W), where 1 watt = 1 joule per second. Power can also be expressed as P = F υ when force and velocity are in the same direction.

→ Simple Machines: Simple machines are devices that make work easier by changing the magnitude or direction of force. They do not reduce total work but help by allowing effort to be applied more conveniently. Examples include levers, pulleys, and inclined planes. They help by increasing force or changing its direction.

→ Mechanical Advantage: Mechanical advantage (MA) is the ratio of load (output force) to effort (input force). MA = Load / Effort. A machine with MA greater than 1 multiplies force, making it easier to lift or move heavy objects. When Mechanical Advantage is less than 1, the machine does not provide force gain. Instead, it provides a gain in speed or distance. Therefore, more effort is required to move the load, but the load moves faster or over a larger distance.

→ Pulley: A pulley is a grooved wheel with a rope used to lift loads. A fixed pulley changes the direction of force but has MA = 1. A movable pulley reduces effort required and provides MA greater than 1. Combined pulley systems (block and tackle) can greatly increase mechanical advantage.

→ Inclined Plane: An inclined plane is a sloping surface used to raise objects with less force. Mechanical advantage is MA = L/ h, where L is the A box being pushed up the ramp length of slope, and h is height. A longer slope reduces required effort but increases distance traveled. It trades force for distance.

→ Lever: A lever is a rigid bar that rotates around a fixed point called the fulcrum. It works on the principle of moments: effort × effort arm = load × load arm. Mechanical advantage is MA = effort arm/load arm. A longer effort arm reduces required force.

→ Classes of Levers: Class I levers have fulcrum in the middle, such as scissors or seesaws. They can multiply force or speed depending on arrangement. Class II levers have load in the middle, such as a wheelbarrow or bottle opener, and always multiply force. Class III levers have effort in the middle, such as tweezers or broom, and they increase speed but require more effort.

→ Energy Conservation in Machines: Machines do not create energy; they only transform it from one form to another or transfer it from one point to another. In ideal machines, work input equals work output. In real machines, some energy is lost due to friction, heat, and sound, so efficiency is always less than 100 percent.
Efficiency = (output work/input work) × 100%.

Work Energy and Simple Machines Notes Class 9

Work

Work is said to be done, when an object is displaced from its position by applying a force.

→ Scientific Conception of Work:

From the point of view of science, following two conditions need to be satisfied for work

1. A force should act on an object.
2. The object must be displaced.

If any one of the above conditions does not exist, work is not said to be done.
e.g. A girl pulls a trolley and the trolley moves through a distance. In this way, she has exerted a force on the trolley and it is displaced. Hence, the work is done.

Work Done by a Constant Force

• Work done by a constant force on an object is equal to the product of the magnitude of the force and the displacement of the object in the direction of force.
• Let us assume that a constant force F is acting on an object and the object is displaced by a distance s in the direction of the force as shown in the figure.
• So, Work done = Force × Displacement in the direction of force
  W = F × s
• The SI unit of work is Newton-metre (N-m) which is also called Joule (J).

Definition of 1 Joule: 1 J is the amount of work done on an object when a force of 1 N displaces it by 1 m along the direction of net force.
1 Joule = 1 Newton × 1 Metre
⇒ 1 J = 1 N-m
1 kJ = 1000 J

Both force (F) and displacement (s) are vector quantities-they have both magnitude and a specific direction.
However, work (W) is a scalar quantity. It has magnitude but no direction in space.

Example 1.
While saving a goal as shown in figure, a goalkeeper’s hand moved back by 15 cm as the stopped a ball while applying a force of 200 N. How much work did the goalkeeper do on the ball in stopping it?
Solution:
The goalkeeper applied a force opposite to the motion of the ball, so she did negative work on the ball. The displacement should be taken as negative becasuse the ball moves in a direction opposite to the direction of the applied force.

Work done by the goalkeeper on the ball = force × displacement of ball in the direction of force
= 200 N × (- 0.15 m) = – 30 J

→ Work from a Force-Displacement Graph

• If we plot the force on an object (y-axis) against displacement in the direction of the force (x-axis), the work done equals the area under the graph.
• For a constant force of 10 N over a displacement of 1 m, the graph is a horizontal line and the area of the shaded rectangle = 10 N × 1 m = 10 J.
• This method is powerful because it works even when the force is not constant – for any force-displacement graph.

Work done = area under the curve

→ Positive, Negative and Zero Work:

• The sign of work done depends on the relative directions of the force and displacement.
• When the force F and displacement s are in the same direction work done will be positive.

i.e. work is done by the force, e.g. A boy pulls an object towards himself.
W = + Fs

When the force F and displacement s are in opposite direction work done will be negative.

i. e. work is done against the force, e.g. Frictional force acts in the direction opposite to the direction of displacement, so work done by friction will be negative.
W = – Fs

When the force and displacement are in perpendicular direction (angle between direction of force and displacement is 90°), work done is zero.

Example 2.
While exercising, a girl lifts a dumbbell and then slowly lowers it down. Identify when she does positive work on the dumbbell and when she does negative work on it.
Solution:
When lifting:
She applies an upward force equal to the weight of the dumbbell. The dumbbell moves upward – force and displacement are in the same direction. She does positive work on the dumbbell.

When lowering:
She still applies an upward force to control the dumbbell, but its displacement is now downward (opposite to the force). She does negative work on the dumbbell.

Example 3.
A crane lifts a crate upwards through a height of 20 m. The lifting force provided by the crane is 5 kN. How much work is done by the force?

Solution:
Given,
force, F = 5 kN = 5000 N
Displacement, s = 20 m,
Work done, W =?
Here, force and displacement are in same direction.
So, W = Fs
= 5000 × 20 = 100000 J
So, the work done by the force is 100000 J or 100 kJ.

→ Work-Energy Theorem

• The work done on an object equals the change in its energy.
• Work Done = Change in Energy W = ∆E
• When positive work is done on an object, it gains energy.
• When negative work is done, it loses energy. This theorem holds even when forces are not constant and even for a system of objects.

→ Consider these everyday examples:

• A fielder throws a cricket ball toward the wickets. The moving ball hits the stumps and makes them fall – the ball had the capacity to do this work.
• A heavy flowerpot raised to a height can damage an object below when it falls – again, the pot has acquired a capacity to do work.
• In each case, the object has acquired a capacity to do work.

Energy

• It is the ability to do work. The energy of an object is measured in terms of its capacity of doing work.
• The SI unit of energy is same as that of work, i.e. Joule (J).
• 1 joule of energy is required to do 1 J of work. A larger unit of energy is kj.

→ Mechanical Energy

• Mechanical energy is the energy an object possesses due to its motion or its position.
• It has two components-kinetic energy (energy of motion) and potential energy (energy of position or configuration). Their sum is the total mechanical energy of the object.

→ Kinetic Energy

• The energy which is possessed by an object due to its motion is called kinetic energy. Its SI unit is joule (J).
• The kinetic energy possessed by an object of mass m, moving with a uniform velocity v is given by
  KE (or E_K) = ½ mv²
• Kinetic energy is equal to the work done on a body to change its velocity.
• The faster an object moves, the more kinetic energy it possesses.

→ Some examples of kinetic energy are

• Due to kinetic energy, a bullet fired from a gun can pierce a target.
• A moving hammer, drives a nail into the wood. Due to its motion, it has kinetic energy or ability to do work.
• A running horse has kinetic energy.
• A flowing river possesses kinetic energy.

→ Derivation of Kinetic Energy Formula:

Consider an object of mass m moving with a uniform velocity u. A force F is applied on it which displaces it through a distance s and it attains a velocity v.

Then, work is done to increase its velocity from u to v.
W = Fs …………………(i)
According to the third equation of motion,
∴ s = \(\frac{v^2-u^2}{2 a}\) ………………..(ii)
where, a is uniform acceleration, u is initial velocity and v is final velocity.
Also from, F = ma ………………… (iii)

Substituting the values of F and s from Eqs. (ii) and (iii) in Eq. (i), we have
W = ma . (\(\frac{v^2-u^2}{2 a}\)) or
W = ½ m (v² – u²)
W = ½ mv² – ½ mu²
If initial velocity, u = 0
Then, W = ½ mv²
This work done is equal to the kinetic energy of the object.
∴ KE (or E_K) = ½ mv²

The SI unit of work and energy, the joule (J), is named in honor of the British physicist James Prescott Joule. Joule’s pioneering research focused on the relationship between mechanical work and heat. He demonstrated that energy can be converted from one form to another, specifically showing that mechanical energy can be transformed into thermal energy.

His work was instrumental in establishing the Law of Conservation of Energy and provided a unified framework for understanding the different manifestations of energy in our universe.

Example 4.
A bullet of mass 8 g is fired with a velocity of 80 ms ^-1. Calculate its kinetic energy.
Solution:
Given, mass, m = 8 g = \(\frac{8}{1000}\) kg and
velocity, v = 80 m/s
KE of the bullet = ½ mv²
= \(\frac{1}{2}\) × \(\frac{8}{1000}\) × (80)²
= \(\frac{1}{2}\) × \(\frac{8}{1000}\) × (80) × 80 = 25.6 J

Example 5.
If a body of mass 5 kg is moving along a straight line with velocity 10 ms^-1 and acceleration 20 ms^-2. Find its kinetic energy (KE) after 10 s.
Solution:
Given, mass of the body, m = 5 kg
Initial velocity, u = 10 ms^-1
Acceleration, a = 20 ms^-2
Time, t = 10 s
First equation of motion, v = u + at ……………….. (i)
KE = ½ mv² [From Eq. (i)]
= ½ m (u + at)^-2
= ½ × 5 × (10 + 20 × 10)^-2
= ½ × 5 × 210 × 210
= 1.1 × 10⁵ J

Example 6.
What is the work done to increase the velocity of a van from 10 m/s to 20 m/s, if the mass of the van is 2000 kg?
Solution:
Given, m = 2000 kg,
v₁ = 10 ms^-1 and
v₂ = 20 ms^-1
The initial kinetic energy of the van
KE₁ = ½ \(v_1^2\)
= ½ × 2000 × (10)²
= 100000 J = 100 kJ
Final kinetic energy of the van
KE₂ = ½ \(v_2^2\)
= ½ × 2000 × (10)²
= 400000 J = 400 kJ
The work done = Change in kinetic energy
= 400 – 100 = 300 kJ
So, the kinetic energy of van increases by 300 kj when it speeds up from 10 ms^-1 to 20 ms^-1.

Potential Energy

The energy possessed by a body due to its change in position or shape is called potential energy.
Its SI unit is joule (J).

→ Potential Energy of an Object at a Height

• The gravitational potential energy of an object at a point above the ground is defined as the work done in raising it from the ground to that point against gravity.
• Consider an object of mass m, lying at a point A on the Earth’s surface. Here, its potential energy is zero and its weight mg acts vertically downwards.
• To lift the object to another position B at a height h, we have to apply a minimum force which is equal to mg in the upward direction.

So, work is done on the body against the force of gravity.
Therefore,
Work done = Force × Displacement
or W =F × s
As, F = mg [weight of the body]
Here, s = h
Therefore, W = mg × h = mgh
i.e. PE = mgh
This work done is equal to the gain in energy of the body. This is the potential energy (PE) of the body.
∴ PE (or E_P) = mgh
where g is acceleration due to gravity (g)

Location	Symbol	Approximate Value
Earth	ge	9.8 m/s2
Moon	gm = \(\frac{g_e}{6}\)	1.63 m/s2

Note:
The potential energy of an object at a height depends on the ground level or zero level you choose.

An object in a given position can have a certain potential energy with respect to one level and a different value of potential energy with respect to another level.

The work done by gravity depends on the difference in vertical heights of the initial and final positions of the objects and not on the path along which the object is moved. It is clear from the figure given below.

In both the situations, irrespective of the path followed the work done on the object is mgh.

Elastic Potential Energy (Spring Systems)

• When we apply an external force to compress or stretch a spring, we perform work to deform its shape.
• This work is stored as energy due to the spring’s configuration.
• Deforming an elastic body requires overcoming its internal restoring forces. When the external force is removed, these forces return the object to its equilibrium shape, transforming stored potential energy into the kinetic energy of the system.

→ Potential Energy in Non-Contact Force Systems:

Energy can also be stored by changing the arrangement of objects that attract or repel each other without touching.

Magnetic Systems:
Separating two unlike poles (N and S) requires work. This work is stored as magnetic potential energy. When released, the magnets accelerate toward each other, converting this stored energy into kinetic energy.

Electrostatic Systems:
Similarly, work is done to separate opposite charges (+ and -). The system of charges possesses energy based on their distance from one another.

Example 7.
Suppose you have a body of mass 1 kg in your hand. To what height will you raise it, so that it may acquire a gravitational potential energy of 1 J? (Take, g = 10 ms^-2)
Solution:
Given, PE = 1 J,
mass, m = 1 kg,
Acceleration due to gravity, g = 10 m^-2,
h = ?
We know that, PE = mgh or
1 = 1 × 10 × h
∴ Height, h = \(\frac{1}{1 \times 10}\)
= 0.1 m = 10 cm

Example 8.
A boy weighing 40 kg climbs up a vertical height of 200 m. Calculate the amount of work done by him. How much potential energy does he gain? (Take, g = 9.8 ms^-2)
Solution:
Given that, mass, m = 40 kg
Acceleration due to gravity, g = 9.8 ms^-2
Height, h = 200 m
Work done by the body = mgh
= 40 × 9.8 × 200 = 78400 J
= 7.84 × 10⁴ J
Gain in PE = Work done = 7.84 × 10⁴ J

Law of Conservation of Energy

• It states that energy can neither be created nor be destroyed, it can only be transformed from one form to another.
• The total energy before and after transformation always remains constant as long as no non-conservative forces (like friction) do work on the object.
• The sum of the kinetic energy and the potential energy of the object is called its mechanical energy.

→ Conservation During Free Fall of a Body:

Consider an object of mass m, lying at position B. It is made to fall freely from a height (h) above the ground, as shown in figure.

The sum of the kinetic energy and the potential energy of the object is called its mechanical energy.

→ At point B:

At the start, the potential energy is mgh and kinetic energy is zero (as its velocity is zero),
i.e. PE = mgh

∴ Total energy, TE = PE + KE = mgh

→ At point A:

As it falls, its potential energy will change into kinetic energy. If v is the velocity of the object at a given instant, its kinetic energy would be ½ mv².
PE = mg (h – x)
From Newton’s third equation of motion,
v² = u² + 2 gx
⇒ v² = 2gx [∵ u = 0]
KE = ½ mv²
= ½ m × 2gx = mgx [∵ v² = 2gx]
∴ Total energy, TE = KE + PE
TE = mgx + mg (h – x) = mgh

→ At point C:

As the fall of the object continues, the potential energy would decrease while the kinetic energy would increase. When the object is about to reach the ground, h~ 0 and v will be the highest.
PE = 0
KE = ½ mv²
= ½ m (2gh) = mgh [∵ v² = 2gh]
∴ Total energy, TE = KE + PE
= mgh + 0 = mgh

At every point during the free fall, the total mechanical energy remains constant and equal to mgh.

The decrease in potential energy at any point in its path appears as an equal amount of increase in kinetic energy.

Thus, we can say that, there is a continuous transformation of gravitational potential energy into kinetic energy.

Example 9.
A 2 kg object is thrown vertically upward with a speed of 10 m/s. What will be its height at the point, where its speed becomes 0 m/s? (At this point, all the kinetic energy will be converted into potential energy)
Solution:
Given,
Mass of the object, m = 2 kg
Initial speed, u = 10 m/s
Gravitational acceleration, g = 9.8 m/s²
The initial kinetic energy is given by
KE = ½ mu²
= ½ × 2 × (10)² = 100 J
At the highest point KE = 0,
so all of the initial kinetic energy becomes potential energy.
PE = KE = 100 J
Potential energy is given by = mgh
Substitute the values,
100 = 2 × 9.8 × h
⇒ 100 = 19.6 × h
h = \(\frac{100}{19.6}\) ≈ 5.1 m.

Example 10.
A man is moving with high velocity of 30 ms¹. Determine the total mechanical energy of the man weighing 60 kg, if he is on a height of 50 m at this speed. (Take, g= 10 ms^-2)
Solution:
Given, mass of man, m = 60 kg
Velocity, v = 30 ms^-1 and
height, h = 50 m
Total energy (TE) of the man at a height of 50 m is given by
TE = PE + KE ………………….(i)
where, PE = mgh and
KE = ½ mv²
TE = mgh + ½ mu² [from Eq. (i)]
= 60 × 10 × 50 + ½ × 60 × (30)2 2
= 30000 + 27000
= 57000 J = 57 kJ

Different Forms of Energy

Energy exists in various forms in nature, each playing a vital role in physical processes. The most common forms include

• Mechanical Energy: The energy possessed by an object due to its motion (kinetic) or its position (potential).
• Thermal Energy: The energy that manifests as heat, making objects warm or hot.
• Light Energy: A form of electromagnetic radiation that enables us to see our surroundings.
• Sound Energy: The energy produced by the vibrations of air or other molecules in a medium.
• Electrical Energy: The energy associated with the position or movement of electrical charges.
• Nuclear Energy: The energy stored within the nuclei of atoms, released during fission or fusion.
• Chemical Energy: The energy stored in the bonds of chemical compounds, such as in food, fuels and batteries.

→ Transformation of Energy

• One form of energy can be converted into other form of energy and this phenomenon is called transformation of energy.
• When an object is dropped from some height, its potential energy continuously converts into kinetic energy. When an object is thrown upwards, its kinetic energy continuously converts into potential energy.

→ Examples of energy transformation are

• Green plants prepare their own food (stored in the form of chemical energy) by using solar energy through the process of photosynthesis.
• When we throw a ball, the muscular energy which is stored in our body, gets converted into kinetic energy of the ball.
• The wound spring in the toy car possesses potential energy. As the spring is released, its potential energy changes into kinetic energy due to which, toy car moves.
• In a stretched bow, potential energy is stored. As it is released, the potential energy of the stretched bow gets converted into the kinetic energy of arrow which moves in the forward direction with large velocity.

→ Some Energy Transformations

Devices	Transformations
Electric motor	Electrical energy into mechanical energy.
Electric generator	Mechanical energy into electrical energy.
Steam engine	Heat energy into kinetic energy.
Electric bulb	Electrical energy into light energy.
Dry cell	Chemical energy into electrical energy.
Solar cell	Light energy into electrical energy.

Rate of Doing Work: Power

• The rate of doing work by an agent or a machine is called the power of the agent or the machine.
  Thus, Power = \(\frac{\text { Work }}{\text { Time }}\)
• If an agent does a total amount of work W by exerting a force on a body for a total time-interval t, then the average power delivered by the agent is given by
  P = W/t

The unit of power is watt (W) in honour of James Watt.
We express larger rate of energy transfer in kilowatt (kW).
1 W = 1 Js^-1
1 kW = 1000 W = 1000 Js^-1
1 MW = 10⁶ W
1 HP (horse power) = 746 W

→ Average Power

• It is defined as the ratio of total work done by the total time taken.
• An agent may perform work at different rates at different intervals of time. In such situation, average power is considered by dividing the total energy consumed by the total time taken.

∴ Average power = \(\frac{\text { Total energy consumed }}{\text { Total time taken }}\)

The unit of power, the watt, is named in honour of James Watt, who developed an efficient steam engine capable of producing rotational motion and driving machinery such as wheels.

Example 11.
A boy does 400 J of work in 20 s and then he does 100 J of work in 2s. Find the ratio of the power delivered by the boy in two cases.
Solution:
Given,
work done by the boy, W₁ = 400 J
Time taken, t₁ = 20 s
Work done by the boy, W₂ = 100 J
Time taken, t₂ = 2 s,
∴ P₁ = \(\frac{W_1}{t_1}\)
= \(\frac{400}{20}\) = 20 W

and P₂ = \(\frac{W_2}{t_2}\)
= \(\frac{100}{2}\) = 50 W

So, \(\frac{P_1}{P_2}\) = \(\frac{20}{50}\) = 2 : 5

Example 12.
A boy of mass 55 kg runs up a staircase of 50 steps in 10 s. If the heigh t of each step is 10 cm, find his power. (Take g = 10 m/s²)
Solution:
Weight of the boy = mg
= 55 × 10 = 550 N
Height ot the staircase,
h = \(\frac{50 \times 10}{100}\) = 5 m
Time taken to climb, t = 10 s
Thus, Power P = \(\frac{\text { Work done }}{\text { Time taken }}\)
= \(\frac{mgh}{t}\)
= \(\frac{550 \times 5}{10}\)

Example 13.
A horse exerts a pull on a cart of 500 N, so that horse cart system moves with a uniform velocity of 36 kmh^-1. What is the power developed by the horse in watt as well as in horse power?
Solution:
Given, force, F = 500 N
and velocity, v = 36 kmh^-1
= \(\frac{36 \times 1000}{3600}\) = 10 ms^-1
As, P = \(\frac{W}{t}\)
= \(\frac{Fs}{t}\) [∵ W = Fs and v = s/t]
= Fv
= 500 × 10 = 5000 W
In horse power, P = \(\frac{5000}{746}\) = 6.70 HP

Machine

• A machine is a device that makes work easier by changing the magnitude or direction of an applied force.
• While a machine cannot reduce the total amount of work required for a task, it allows us to apply a smaller effort over a longer distance, or to change the direction of force to a more convenient one.

→ Classification of Machines

Simple machines are generally categorised into three main types based on their mechanical principles.

→ Terms Related to Machine

The terms related to machine are as follows

• Load: It is the resistive or opposing force against which the machine works. It is denoted by L.
• Effort: It is the force applied on the machine to overcome the load. It is denoted by E.
• Mechanical Advantage (MA): It is the ratio of the load to the effort. It is denoted by MA.
• It is expressed as, MA = \(\frac{L}{E}\)
• If MA > 1 (i.e. L > E), the machine acts as a force multiplier – a smaller effort is able to move a much larger load.
• For example, a carjack lifts a heavy vehicle with little effort and pulleys are used to hoist large weights where the effort required is significantly less than the load.
• If MA < I (i.e. L < E), the machine acts as a speed multiplier – a small movement of effort produces a larger, faster movement of the load.
• For example, the blades of scissors move a greater distance than the handles.
• If MA = 1 (i.e. L = E), the machine acts as a direction changer – the effort equals the load, but the direction of force is changed to a more convenient one. For example, a fixed pulley lets you pull downward to lift a load upward.

→ In every case, the total work done remains constant

• A higher mechanical advantage means less effort is needed but over a greater distance.
• A lower mechanical advantage means more effort is needed, but the load moves over a greater distance.
• When MA = 1, effort and distance remain unchanged – only the direction of force is altered.

The Pulley

• A pulley is a simple machine consisting of a wheel with a grooved rim that guides a rope, string, or cable.
• Pulleys are widely used in cranes, elevators, and flagpoles.

They are primarily classified into two types

→ Fixed Pulley

• A pulley whose axis of rotation is fixed in position to a rigid support is called a fixed pulley. In this system, the pulley does not move up or down with the load.
• It is used to change the direction of the applied effort to a more convenient one. It is easier for a person to pull downward using their own body weight than to lift a load by applying an upward force directly.
• Thus, even though a fixed pulley does not reduce the magnitude of force required (MA = 1, i.e. E = L), it provides convenience by making the direction of effort more practical.
• A common example is drawing water from a well, where pulling down on the rope raises the bucket upward.

→ Movable Pulley

• A pulley whose axis of rotation is not fixed and moves along with the load is called a movable pulley. In this arrangement, one end of the rope is attached to a fixed support, while the effort is applied to the free end.
• It acts as a force multiplier. The load is supported by two segments of the rope, effectively halving the effort required to lift it, meaning an effort of 50 N can lift a load of 100 N, giving a mechanical advantage of 2.
• Systems with multiple pulleys can achieve even higher MA values.
• Heavy-duty cranes or modern elevator systems use this system where multiple pulleys move to assist in lifting massive weights.

→ The Inclined Plane

• An inclined plane is a flat supporting surface tilted at an angle, with one end raised higher than the other. Examples include ramps, slides, and winding hilly roads.
• It allows a heavy load to be raised to a certain height by applying a smaller force over a longer distance.
• Work-Energy Relationship Pushing an object up a smooth incline at a constant speed requires work equivalent to the potential energy gained.

• The Work Principle Work done (W) is the product of force (F) and displacement (s)
  W = F × s
• For any ideal machine, the work done remains constant. This creates a fundamental tradeoff
  If Force ↓, then Displacement ↑
• A machine allows us to use less effort, but we must apply that effort over a proportionally longer distance.

→ Mathematical Formulation

By the Work-Energy theorem (ignoring friction)

Work done by effort = Potential energy gained
Effort × length of plane = Load × height
F × L = mg × h
Rearranging to find the mechanical advantage,
MA = \(\frac{Load (m g)}{{Effort}\left(F^{\prime}\right)}\)
= \(\frac{L}{h}\)

Since, the length (L) is the hypotenuse and is always greater than the height (h), the MA of an inclined plane is always greater than 1.

By increasing the length of the inclined plane and reducing its angle of inclination, the effort (F) required to move an object is significantly decreased, though the displacement over which the force is applied increases.

Example 1.
A box is pushed up a wooden ramp to a height of 30 cm. If the ramp is 50 cm long, what is the mechanical advantage?
Solution:
Given, Height (h) = 30 cm,
Width (base) = 40 cm
Length of the plane, L = \(\sqrt{h^2+\text { base }^2}\)
= \(\sqrt{30^2+40^2}\)
= \(\sqrt{900+1600}\)
= \(\sqrt{2500}\)
L = 50 cm
Mechanical Advantage, MA = \(\frac{L}{h}\)
MA = \(\frac{50}{30}\)
MA ≈ 1.67

The Lever

A lever is a rigid bar or rod that can rotate or turn about a fixed point. It is one of the most common simple machines used to lift heavy objects.

→ Components of a Lever:

• Fulcrum (F): It is the fixed pivot point about which the lever rotates.
• Load (L): It is the force to be overcome or the object to be lifted.
• Effort (E): It is the force applied by the user on the lever.
• Load Arm: It is the perpendicular distance from the fulcrum to the load.
• Effort Arm: It is the perpendicular distance from the fulcrum to the effort.

→ Principle of a Lever:

A lever allows a smaller effort to lift a much heavier load by utilizing the length of its arms. In an ideal lever, this balance is expressed as
Effort × Effort arm = Load × Load arm

This works because of the trade-off between force and distance. By increasing the length of the effort arm, a smaller effort F₁ applied over a larger distance d1 is converted into a larger force F₂ acting over a smaller distance d₂ as
F₁ × d₁ = F₂ × d₂

The Mechanical Advantage (MA) of a lever is defined as the ratio of the load to the effort, which is also equivalent to the ratio of the effort arm to the load arm
MA = \(\frac{\text { Load }}{\text { Effort }}\)
= \(\frac{\text { Load arm }}{\text { Effort arm }}\)
= \(\frac{d_1}{d_2}\)

Key Principles

• By increasing the length of the effort arm relative to the load arm, the lever acts as a force multiplier (F₂ > F₁).
• While the required effort is reduced, it must be applied over a proportionally larger distance. This ensures that the total work done remains constant, consistent with the law of conservation of energy.

Classes of Levers

Levers are classified into three categories based on the relative position of the Fulcrum, Load, and Effort.

1. Class I Lever

• Position: The fulcrum is located between the load and the effort.
• MA Value: Can be > 1, < 1, or = 1.
  Examples: Scissors, see-saw, crowbar, balance scale.

2. Class II Lever

• Position: The load is located between the fulcrum and the effort.
• MA Value: Always > 1 (Because the effort arm is always longer than the load arm. Acts as a force multiplier).
• Examples: Wheelbarrow, bottle opener, lemon squeezer.

Why is a door handle placed at the edge, far away from the hinges?
A door is a Class II lever where the hinge is the fulcrum and the door itself is the load. By placing the handle far from the hinges, you maximize the effort arm. This increases the mechanical advantage, allowing you to open a heavy door with very little force.

3. Class III Lever

• Position The effort is located between the fulcrum and the load.
• MA Value Always < 1 (Because the load arm is always longer than the effort arm. Acts as a speed/distance multiplier).
• Examples Tweezers, tongs, hammer, oar.

Example 2.
On a see-saw, child A (15 kg) sits 2 m away from the fulcrum. Where must child B (30 kg) sit on the other side to balance it?
Solution:
Applying the principle of working of a lever
Effort × effort arm = Load × load arm
15 × 2 = 30 × L
⇒ 30 = 30 × L
⇒ L = 1 m
Child B must sit exactly 1 m away from the fulcrum.

→ Energy Conservation and Machines

• Machines obey the Law of Conservation of Energy.
• The total work put into a machine (input) is equal to the useful work done by the machine (output) plus the work lost due to friction.

Machines do not create energy:
They simply transfer energy from one place to another or change its form, making the task practically easier for humans.

• In the Himalayan regions, people have long utilised the potential energy of water flowing downhill.
• As water flows down a pipe, its potential energy converts to kinetic energy.
• This kinetic energy strikes a turbine wheel of a Gharat (Watermill) setting it into rotational motion to grind grain.
• This demonstrates natural energy conversion aiding human labor without “creating” new energy.

→ The Myth of Perpetual Motion

• Throughout history, inventors have tried to build “perpetual motion machines”, devices that run forever and do continuous work without fuel.
• However all real machines have moving parts that generate friction. Energy is constantly dissipated as heat and sound. Therefore, all real machines eventually slow down and stop if no external energy is supplied.
• Building such a machine would require creating energy from nothing, which directly violates the law of conservation of energy.

The post Work Energy and Simple Machines Class 9 Notes Science Chapter 7 appeared first on Learn CBSE.

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