Simple Machine 8

                                                             Simple Machine

🛠️ Technical Terms for Simple Machines

Term	Definition
Simple Machine	A device that changes the magnitude or direction of a force to make work easier.
Effort	The force applied to a machine to perform work.
Load	The object or resistance that needs to be moved or lifted by a machine.
Fulcrum	The fixed point around which a lever rotates.
Mechanical Advantage (MA)	The ratio of the load to the effort applied in a machine.
Velocity Ratio (VR)	The ratio of the distance moved by the effort to the distance moved by the load.
Efficiency	The ratio of useful output work to the input work, expressed as a percentage.
Effort Arm	The distance between the effort and the fulcrum in a lever.
Load Arm	The distance between the load and the fulcrum in a lever.
Inclined Plane	A flat surface set at an angle to reduce the effort needed to lift an object.
Wedge	A double-inclined plane used to split or lift objects.
Screw	An inclined plane wrapped around a cylinder, used to hold objects together or lift them.
Pulley	A wheel with a rope or chain that helps lift objects or change the direction of force.
Fixed Pulley	A pulley attached to a stationary object; changes the direction of force but not the effort.
Movable Pulley	A pulley that moves with the load, reducing the effort needed to lift it.
Block and Tackle	A system of fixed and movable pulleys used together to increase mechanical advantage.
Wheel and Axle	A circular object (wheel) connected to a rod (axle) that multiplies force or speed.
Input Force	The force applied to a machine.
Output Force	The force exerted by a machine on the load.
Work Done	The product of force and the distance over which the force acts. Formula: $W = F \times d$
Friction	The resistance between two surfaces that reduces efficiency in a machine.
Ideal Machine	A machine with 100% efficiency (no friction or energy loss).
Actual Machine	A machine that loses some energy due to friction and other factors.
Pitch	The distance between two threads in a screw.
Circumference	The distance around a circle (used in screws and wheels). Formula: $C = 2 \pi r$
First Class Lever	A lever where the fulcrum is between the effort and the load (e.g., see-saw).
Second Class Lever	A lever where the load is between the fulcrum and the effort (e.g., wheelbarrow).
Third Class Lever	A lever where the effort is between the fulcrum and the load (e.g., tongs).
Load Distance	The distance the load moves when the machine is used.
Effort Distance	The distance the effort moves when the machine is used.
Lever Arm	The length of the lever from the fulcrum to the point where the force is applied.
Trade-off	The relationship between force and distance in simple machines; increasing one decreases the other.
Compound Machine	A machine that combines two or more simple machines (e.g., scissors = lever + wedge).
Input Work	The work done on a machine.
Output Work	The useful work done by a machine.
Direction of Force	The path along which a force is applied to an object.
Mechanical System	A system that consists of several connected machines working together.

✅ ✅ ✅ Summary of Formulas

Type of Machine	Formula
Lever	Effort × Effort Arm = Load × Load Arm
Pulley	MA = Number of Supporting Ropes
Inclined Plane	MA = Length ÷ Height
Wheel and Axle	MA = Radius of Wheel ÷ Radius of Axle
Screw	MA = Circumference ÷ Pitch
Wedge	MA = Length ÷ Width
Efficiency	(Output Work ÷ Input Work) × 100

🌟 What are Simple Machines?

• Simple machines are basic mechanical devices used to make work easier by:
  ✔️ Reducing the effort needed to do work.
  ✔️ Changing the direction of the applied force.
  ✔️ Increasing the speed or distance of movement.
• Simple machines do not reduce the total amount of work but make it easier by distributing the force more efficiently.

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🔎 Types of Simple Machines

There are six main types of simple machines:

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1. 🏋️‍♂️ Lever

A lever is a rigid bar that rotates around a fixed point called the fulcrum. It helps lift or move heavy loads with less effort.

📌 Parts of a Lever:

• Fulcrum – Fixed point where the lever rotates.
• Effort – Force applied to move the lever.
• Load – Object or resistance to be moved.

🛠️ Types of Levers:

Type	Description	Example
First Class Lever	Fulcrum is between the load and effort.	See-saw, scissors, pliers
Second Class Lever	Load is between the fulcrum and effort.	Wheelbarrow, bottle opener
Third Class Lever	Effort is between the fulcrum and load.	Fishing rod, tongs, tweezers

🧠 Formula:

$$\text{Effort} \times \text{Effort arm} = \text{Load} \times \text{Load arm}$$

1. Class 1 Lever

➡️ The fulcrum is located between the load and the effort.
➡️ It can provide either a mechanical advantage greater than or less than 1, depending on the position of the fulcrum.

✅ Examples:

• Seesaw
• Scissors
• Crowbar

✅ Formula:

$$\text{MA} = \frac{\text{Effort Arm}}{\text{Load Arm}}$$

✅ Diagram:

Effort → Fulcrum → Load

Effort ——⚫—— Load
         ↑
     Fulcrum

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2. Class 2 Lever

➡️ The load is located between the fulcrum and the effort.
➡️ Always provides a mechanical advantage greater than 1 (makes work easier).

✅ Examples:

• Wheelbarrow
• Nutcracker
• Bottle opener

✅ Formula:

$$\text{MA} > 1$$

✅ Diagram:

Fulcrum → Load → Effort

Fulcrum ——⚫—— Effort
         ↑
        Load

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3. Class 3 Lever

➡️ The effort is located between the load and the fulcrum.
➡️ Always provides a mechanical advantage less than 1 (increases speed and range of motion).

✅ Examples:

• Fishing rod
• Tweezers
• Human arm

✅ Formula:

$$\text{MA} < 1$$

✅ Diagram:

Fulcrum → Effort → Load

Fulcrum ——⚫—— Load
         ↑
        Effort

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🌟 Difference Between Types of Levers

Feature	Class 1 Lever	Class 2 Lever	Class 3 Lever
Position of Fulcrum	Between load and effort	At one end, load between fulcrum and effort	At one end, effort between fulcrum and load
Mechanical Advantage (MA)	MA can be >1 or <1	MA > 1	MA < 1
Function	Can be used for force or speed gain	Always multiplies force	Increases speed and range
Examples	Seesaw, scissors, crowbar	Wheelbarrow, nutcracker, bottle opener	Fishing rod, tweezers, human arm

✅ Example:

• If a load of 10 N is placed 2 m from the fulcrum, and the effort arm is 4 m, the effort needed is:

$$\text{Effort} = \frac{10 \times 2}{4} = 5 \, N$$

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2. 🪢 Pulley

A pulley is a wheel with a rope or chain wrapped around it. It helps lift heavy objects by changing the direction of the applied force.

🛠️ Types of Pulleys:

Type	Description	Example
Fixed Pulley	Changes the direction of force; no mechanical advantage.	Flagpole
Movable Pulley	Reduces effort; mechanical advantage = 2.	Construction crane
Block and Tackle	Combination of fixed and movable pulleys; increases mechanical advantage.	Sailboat rigging

✅ Formula:

$$\text{Mechanical Advantage} = \text{Number of supporting ropes}$$

Types of Pulleys:

1. Fixed Pulley:

   • Description: In a fixed pulley, the wheel is fixed in a single position, and the rope is passed over it. The load remains stationary while the force is applied in a different direction.
   • Example: A flagpole uses a fixed pulley to raise and lower the flag.
   • Mechanical Advantage: 1 (no mechanical advantage, only changes the direction of force).

2. Movable Pulley:

   • Description: In a movable pulley, the wheel is not fixed but moves along with the load. The rope is attached to a fixed point at one end, and the load is connected to the movable pulley.
   • Example: A construction crane uses movable pulleys to lift heavy materials.
   • Mechanical Advantage: Greater than 1 (it reduces the effort needed to lift the load).

3. Compound Pulley (Block and Tackle):

   • Description: A compound pulley system combines fixed and movable pulleys to give a mechanical advantage and reduce the force needed to lift a heavy load.
   • Example: A well pulley system that allows a person to pull up water from a well.
   • Mechanical Advantage: More than 1 (depends on the number of pulleys in the system).

🛠️  Difference between Fixed, Movable, and Compound Pulleys:

Type	Description	Mechanical Advantage	Example
Fixed Pulley	The pulley is stationary, and the load moves.	1	Flagpole, elevator system
Movable Pulley	The pulley moves with the load.	Greater than 1	Crane lifting heavy materials
Compound Pulley	A combination of fixed and movable pulleys.	More than 1	Block and tackle system, well pulley system

✅   Diagram of Pulleys:

1. Fixed Pulley:

    |------|        |---------|
    | Load |<--->| Pulley Wheel |
    |------|        |---------|
                      ^
                  Rope Path

2. Movable Pulley:

    |------|          |---------|          |------|
    | Load |<----->| Pulley Wheel |<----->| Fixed |
    |------|          |---------|          | Support|
                               ^
                           Rope Path

3. Compound Pulley (Block and Tackle):

      |---------|       |---------|      |---------|
      | Load    |<--->| Pulley  |<--->| Pulley  |
      |---------|       | Wheel   |      | Wheel   |
                              ^
                          Rope Path

Example:

Let's say you need to lift a heavy box (the load). If you use a fixed pulley, you’ll only be able to change the direction of the force, so you'll have to pull the rope down to lift the box up. If you use a movable pulley, you can apply less force because the pulley moves with the box, making it easier to lift. Using a compound pulley, you can lift even heavier loads with less effort because the system combines both fixed and movable pulleys.

Conclusion:

• Fixed pulleys are simple and useful when you only need to change the direction of the force.
• Movable pulleys are great for reducing the amount of effort needed.
• Compound pulleys combine multiple pulleys to make lifting much easier, especially for very heavy loads.
• ✅ Example:

• In a block and tackle system with 3 ropes, the mechanical advantage is:

$$\text{MA} = 3$$

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3. 🏔️ Inclined Plane

An inclined plane is a flat surface set at an angle. It helps lift objects by spreading the effort over a longer distance.

✅ Formula:

$$\text{Mechanical Advantage} = \frac{\text{Length of inclined plane}}{\text{Height of inclined plane}}$$

✅ Example:

• If an inclined plane is 5 m long and 1 m high, the mechanical advantage is:

$$\frac{5}{1} = 5$$

🛠️ Example Machines:

• Ramps
• Stairs
• Sloping roads

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4. 🚲 Wheel and Axle

A wheel and axle is a circular object (wheel) attached to a rod (axle). It reduces the effort needed to rotate or move an object.

✅ Formula:

$$\text{Mechanical Advantage} = \frac{\text{Radius of Wheel}}{\text{Radius of Axle}}$$

✅ Example:

• If the radius of the wheel is 30 cm and the axle is 5 cm, the mechanical advantage is:

$$\frac{30}{5} = 6$$

🛠️ Example Machines:

• Steering wheel
• Door knob
• Bicycle

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5. 🔩 Screw

A screw is an inclined plane wrapped around a cylinder. It converts rotational force into linear force.

✅ Formula:

$$\text{Mechanical Advantage} = \frac{\text{Circumference of screw}}{\text{Pitch of screw}}$$

• Circumference = $2 \pi r$
• Pitch = Distance between threads

🛠️ Example Machines:

• Bottle cap
• Drill
• Screw jack

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6. 🔪 Wedge

A wedge is a double-inclined plane used to split or lift objects.

✅ Formula:

$$\text{Mechanical Advantage} = \frac{\text{Length of wedge}}{\text{Width of wedge}}$$

✅ Example:

• If a wedge is 10 cm long and 2 cm wide, the mechanical advantage is:

$$\frac{10}{2} = 5$$

🛠️ Example Machines:

• Knife
• Axe
• Chisel

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🎯 Mechanical Advantage (MA)

Mechanical Advantage measures how much a machine multiplies the applied effort.

$$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

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🚀 Efficiency of a Machine

No machine is 100% efficient due to friction and other losses.

$$\text{Efficiency} = \frac{\text{Output Work}}{\text{Input Work}} \times 100$$

✅ Example:

• If input work = 100 J and output work = 80 J:

$$\text{Efficiency} = \frac{80}{100} \times 100 = 80\%$$

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🔥 Key Differences Between Types of Simple Machines

Type	Function	Example
Lever	Rotates around a fulcrum	Scissors, crowbar
Pulley	Changes direction of force	Flagpole, crane
Inclined Plane	Reduces lifting effort	Ramp, slide
Wheel and Axle	Rotational force	Car wheel, doorknob
Screw	Converts rotation into force	Drill, bolt
Wedge	Splits or cuts objects	Axe, knife

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💡 Why Are Simple Machines Important?

✔️ Reduce the amount of force needed to do work.
✔️ Increase speed or distance of movement.
✔️ Change the direction of applied force.
✔️ Make work more efficient and easier.

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✅ ✅ ✅ Summary of Formulas

Type of Machine	Formula
Lever	Effort × Effort Arm = Load × Load Arm
Pulley	MA = Number of Supporting Ropes
Inclined Plane	MA = Length ÷ Height
Wheel and Axle	MA = Radius of Wheel ÷ Radius of Axle
Screw	MA = Circumference ÷ Pitch
Wedge	MA = Length ÷ Width
Efficiency	(Output Work ÷ Input Work) × 100

🛠️Technical term;

1. Simple Machine

A simple machine is a basic mechanical device that helps make work easier by:
✅ Increasing or decreasing the force needed.
✅ Changing the direction of the force.
✅ Increasing the distance or speed of movement.

✅ Examples:

• Lever
• Pulley
• Inclined Plane
• Wheel and Axle
• Wedge
• Screw

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🏋️‍♂️ 2. Effort

The effort is the force applied to a machine to perform work.

• Measured in Newtons (N).
• The machine reduces the effort needed by multiplying the applied force.

✅ Example:

• When you push down on a lever, the force you apply is the effort.

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🎯 3. Load

The load is the object or resistance that needs to be moved or lifted.

• Also measured in Newtons (N).

✅ Example:

• Lifting a stone with a lever — the stone is the load.

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🔄 4. Fulcrum

The fulcrum is the fixed point around which a lever rotates.

• The position of the fulcrum determines the type of lever and its mechanical advantage.

✅ Example:

• In a see-saw, the central point where the board balances is the fulcrum.

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🚀 5. Mechanical Advantage (MA)

The Mechanical Advantage is the ratio of the output force (load) to the input force (effort).

$$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

✅ Example:

• If you use a lever to lift a 20 N load with 5 N of effort:

$$\text{MA} = \frac{20}{5} = 4$$

👉 This means the machine multiplies the effort 4 times!

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⚡ 6. Velocity Ratio (VR)

The Velocity Ratio is the ratio of the distance moved by the effort to the distance moved by the load.

$$\text{VR} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$$

✅ Example:

• If the effort moves 2 m while the load moves 0.5 m:

$$\text{VR} = \frac{2}{0.5} = 4$$

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🌟 7. Efficiency

Efficiency measures how effectively a machine converts input work into useful output work.

$$\text{Efficiency} = \frac{\text{Output Work}}{\text{Input Work}} \times 100$$

✅ Example:

• If input work = 100 J and output work = 80 J:

$$\text{Efficiency} = \frac{80}{100} \times 100 = 80\%$$

📏 8. Effort Arm

The Effort Arm is the distance between the effort and the fulcrum in a lever.

• A longer effort arm reduces the effort needed.

✅ Example:

• In a crowbar, the longer the handle (effort arm), the less effort you need to lift an object.

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📏 9. Load Arm

The Load Arm is the distance between the load and the fulcrum in a lever.

• A shorter load arm increases mechanical advantage.

✅ Example:

• In a seesaw, if the load is closer to the fulcrum, less effort is needed to lift it.

🎯    Relation among MA, VR and Efficiency

The relationship among Mechanical Advantage (MA), Velocity Ratio (VR), and Efficiency (η) in a machine is given by the formula:

$$\eta = \frac{\text{MA}}{\text{VR}} \times 100$$

where:

• $\eta$ = Efficiency (%)
• MA = Mechanical Advantage
• VR = Velocity Ratio

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✅ Explanation:

1. Mechanical Advantage (MA):

   • It tells how much the machine multiplies the input force.
   • Higher MA means the machine reduces the effort needed.
   • Formula:
   $$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

2. Velocity Ratio (VR):

   • It tells how much the machine multiplies the distance or speed of the input force.
   • Formula:
   $$\text{VR} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$$

3. Efficiency (η):

   • It measures how well the machine converts input work into useful output work.
   • Efficiency can’t exceed 100% because of friction and energy loss.
   • Formula:
   $$\eta = \frac{\text{Output Work}}{\text{Input Work}} \times 100$$

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🏆 Derivation:

Since:

$$\text{Input Work} = \text{Effort} \times \text{Distance moved by effort}$$

and

$$\text{Output Work} = \text{Load} \times \text{Distance moved by load}$$

Therefore,

$$\eta = \frac{\frac{\text{Load}}{\text{Effort}} \times \frac{\text{Distance moved by load}}{\text{Distance moved by effort}}}{1} \times 100$$ $$\eta = \frac{\text{MA}}{\text{VR}} \times 100$$

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🌟 Conclusion:

👉 If MA = VR, efficiency = 100% (Ideal Machine).
👉 In real life, due to friction and other losses, efficiency is less than 100%.

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🚀 Example:

A machine has:

• Mechanical Advantage (MA) = 4
• Velocity Ratio (VR) = 5

$$\eta = \frac{4}{5} \times 100 = 80\%$$

👉 The machine is 80% efficient.

🔥 1. Ideal Machine vs Practical Machine

Feature	Ideal Machine	Practical Machine
Definition	A machine that has 100% efficiency (no energy loss)	A machine that has efficiency less than 100% due to friction and energy loss
Friction	No friction	Friction is present
Efficiency	100% (η = 1)	Less than 100% (η < 1)
Output Work	Output work = Input work	Output work < Input work
Energy Loss	No energy is lost as heat, sound, or vibration	Some energy is lost as heat, sound, and vibration
Example	Theoretical lever, pulley, wheel, etc.	Actual lever, pulley, wheel, etc.
Mechanical Advantage	MA = VR	MA < VR

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🚀 2. Key Differences

👉 In an Ideal Machine, all input energy is converted into useful output.
👉 In a Practical Machine, some input energy is lost due to friction and other resistances.

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🏆 3. Formulas

✅ For an Ideal Machine:

• Efficiency = 100%

$$\eta = \frac{\text{MA}}{\text{VR}} \times 100 = 100\%$$

• Mechanical Advantage = Velocity Ratio

$$\text{MA} = \text{VR}$$

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✅ For a Practical Machine:

• Efficiency is less than 100%

$$\eta = \frac{\text{MA}}{\text{VR}} \times 100 < 100\%$$

• Mechanical Advantage < Velocity Ratio

$$\text{MA} < \text{VR}$$

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🌟 4. Example

✅ Ideal Machine Example:

➡️ A frictionless pulley system where effort is exactly equal to the load’s resistance divided by the number of pulleys.

$$\text{MA} = \text{VR} = 4$$

Efficiency = 100%

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✅ Practical Machine Example:

➡️ A real pulley system where friction reduces the output work.
If:

• MA = 3
• VR = 4

$$\eta = \frac{3}{4} \times 100 = 75\%$$

Efficiency = 75%

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🎯 5. Key Points

✅ An Ideal Machine is a theoretical concept; in reality, no machine is ideal.
✅ A Practical Machine always has efficiency less than 100%.
✅ The more friction and energy loss, the lower the efficiency.
✅ Lubrication and smoother surfaces can reduce friction and increase efficiency.

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🖼️ 6. Image

Here’s a simple diagram to explain the difference visually:

✅ Ideal vs Practical Machine

• Ideal Machine = No friction, full energy transfer
• Practical Machine = Energy loss due to friction

Here's a visual comparison of an Ideal Machine vs Practical Machine! 🔥

• Left side: Ideal Machine – No friction, 100% efficiency, equal input and output work.
• Right side: Practical Machine – Friction, energy loss (heat and sound), and lower efficiency.

🔥 Numerical Problems on MA, VR, and Efficiency

Let’s go through a few examples step-by-step! 😎

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Example 1:

A machine has a Mechanical Advantage (MA) of 4 and a Velocity Ratio (VR) of 5. Find the efficiency of the machine.

✅ Given:

• MA = 4
• VR = 5

✅ Formula:

$$\eta = \frac{\text{MA}}{\text{VR}} \times 100$$

✅ Solution:

$$\eta = \frac{4}{5} \times 100$$ $$\eta = 0.8 \times 100 = 80\%$$

✅ Answer:

👉 Efficiency of the machine = 80%

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Example 2:

A lever has a velocity ratio of 3 and an efficiency of 75%. Find the mechanical advantage of the lever.

✅ Given:

• VR = 3
• η = 75%

✅ Formula:

$$\text{MA} = \frac{\eta \times \text{VR}}{100}$$

✅ Solution:

$$\text{MA} = \frac{75 \times 3}{100}$$ $$\text{MA} = \frac{225}{100} = 2.25$$

✅ Answer:

👉 Mechanical Advantage = 2.25

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Example 3:

A pulley system is used to lift a load of 500 N by applying an effort of 125 N. If the velocity ratio is 5, calculate:

1. Mechanical Advantage
2. Efficiency

✅ Given:

• Load = 500 N
• Effort = 125 N
• VR = 5

✅ Formulas:

$$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$ $$\eta = \frac{\text{MA}}{\text{VR}} \times 100$$

✅ Solution:

1. Mechanical Advantage:

$$\text{MA} = \frac{500}{125} = 4$$

2. Efficiency:

$$\eta = \frac{4}{5} \times 100$$ $$\eta = 0.8 \times 100 = 80\%$$

✅ Answer:

👉 Mechanical Advantage = 4
👉 Efficiency = 80%

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Example 4:

A machine with a velocity ratio of 6 has an efficiency of 60%. Find the effort needed to lift a load of 360 N.

✅ Given:

• VR = 6
• η = 60%
• Load = 360 N

✅ Formulas:

$$\text{MA} = \frac{\eta \times \text{VR}}{100}$$ $$\text{Effort} = \frac{\text{Load}}{\text{MA}}$$

✅ Solution:

1. Mechanical Advantage:

$$\text{MA} = \frac{60 \times 6}{100} = \frac{360}{100} = 3.6$$

2. Effort:

$$\text{Effort} = \frac{360}{3.6} = 100 \, \text{N}$$

✅ Answer:

👉 Effort required = 100 N

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✅✅✅ Key Formulas Recap:

1. Mechanical Advantage (MA):

$$\text{MA} = \frac{\text{Load}}{\text{Effort}}$$

2. Velocity Ratio (VR):

$$\text{VR} = \frac{\text{Distance moved by effort}}{\text{Distance moved by load}}$$

3. Efficiency (η):

$$\eta = \frac{\text{MA}}{\text{VR}} \times 100$$

✅     Summary of Differences:

Type of Simple Machine	Description	Mechanical Advantage	Example
Lever	A rigid bar that rotates around a fixed point (fulcrum).	Depends on fulcrum position.	Crowbar, seesaw
Inclined Plane	A flat surface tilted at an angle to reduce lifting effort.	Greater with a larger angle.	Ramp, slide
Wheel and Axle	A wheel attached to a smaller axle that rotates together.	Depends on wheel to axle radius ratio.	Doorknob, bicycle
Pulley	A wheel with a rope running along a groove to lift loads.	Depends on the number of pulleys used.	Flagpole, crane
Screw	An inclined plane wrapped around a central shaft.	Greater with closer threads.	Screw, jar lid
Wedge	A pointed object used to split or lift material.	Greater with a sharper and thinner wedge.	Knife, axe