Mechanical Advantage and Simple Machines PDF

Mechanical Advantage and Simple Machines Mechanical QCSH Robotics II Objectives: At the end of the session, you are expected to: a. Define and explain mechanical advantage. b. Calculate AMA and IMA for various simple machines. c...

Mechanical Advantage and Simple Machines Mechanical QCSH Robotics II Objectives: At the end of the session, you are expected to: a. Define and explain mechanical advantage. b. Calculate AMA and IMA for various simple machines. c. Understand the relationship between mechanical advantage and efficiency. Mechanical QCSH Robotics II Simple Machines Simple machines are basic mechanical devices that make tasks easier by magnifying the applied force, changing its direction, or both. They are the building blocks of more complex machines and have been utilized since ancient times to accomplish tasks efficiently. Simple machines help reduce the effort needed to perform work by providing a mechanical advantage. Mechanical QCSH Robotics II Simple Machines Wheel and Lever Axle Inclined Plane Pulley Wedge Screw Mechanical QCSH Robotics II Simple Machines Lever A rigid bar that pivots around a fixed point called the fulcrum. Levers are used to lift heavy objects or apply force with less effort. Examples: Seesaws, crowbars, scissors, and bottle openers. Mechanical QCSH Robotics II Simple Machines A wheel with a groove along its edge, through which a rope or cable can run. Pulleys are used to lift or lower loads with ease and can be combined in systems to increase mechanical advantage. Examples: Cranes, Pulley flagpoles, window blinds, and elevators Mechanical QCSH Robotics II Simple Machines A larger wheel attached to a Wheel and smaller axle, allowing them to Axle rotate together. This setup reduces friction and makes it easier to move or lift objects. Examples: Door knobs, rolling carts, car steering wheels, and windmills Mechanical QCSH Robotics II Simple Machines A flat surface set at an angle to the horizontal. Inclined planes allow heavy objects to be moved upward or downward with less effort, Inclined Plane spreading the effort over a longer distance. Examples: Ramps, slides, and sloping roads. Mechanical QCSH Robotics II Simple Machines A device made up of two inclined planes that come together to form a sharp edge. Wedges are used to split, cut, or lift objects by applying force to a smaller area. Examples: Knives, axes, chisels, and doorstops. Wedge Mechanical QCSH Robotics II Simple Machines A spiral-shaped inclined plane wrapped around a cylinder or cone. Screws convert rotational force into linear motion and are used to hold materials together or lift objects. Screw Examples: Bolts, jar lids, clamps, and jackscrews Mechanical QCSH Robotics II Mechanical Advantage Mechanical advantage is a crucial concept in physics and engineering, particularly in the analysis of simple machines. It refers to the ratio of the output force produced by a machine to the input force applied to it. This measurement helps in understanding how effectively a machine amplifies force. Mechanical QCSH Robotics II Mechanical Advantage Mechanical QCSH Robotics II Mechanical Advantage There are two types of Mechanical Advantage: 1. Actual Mechanical Advantage (AMA) 2. Ideal Mechanical Advantage (IMA) Mechanical QCSH Robotics II Mechanical Advantage There are two types of Mechanical Advantage: 1. Actual Mechanical Advantage (AMA): Considers real-world factors like friction and inefficiencies. 2. Ideal Mechanical Advantage (IMA): Assumes a perfect system without energy losses. Mechanical QCSH Robotics II Mechanical Advantage The Actual Mechanical Advantage (AMA) reflects the real-world performance of a machine. It is defined as the ratio of the output force (the force exerted by the machine) to the input force (the force applied to the machine). Mechanical QCSH Robotics II Mechanical Advantage The Ideal Mechanical Advantage (IMA) is a theoretical value that assumes no energy is lost to friction or deformation. It is based solely on the distances moved by the input and output forces. Mechanical QCSH Robotics II Mechanical Advantage 200 N 50 N Mechanical QCSH Robotics II Mechanical Advantage Example: Imagine you are using a lever to lift a 200 N weight. You need to apply a force of 50 N to lift it. What is the AMA? This means the lever multiplies your input force by 4. Mechanical QCSH Robotics II Mechanical Advantage 200 N 50 N Mechanical QCSH Robotics II Mechanical Advantage Example: Suppose a lever has an input arm 2 meters long and an output arm 0.5 meters long. What is the IMA? This means the lever multiplies your input force by 4. Mechanical QCSH Robotics II Mechanical Advantage Note: Since the Ideal Mechanical Advantage assumes no energy loss, it is always greater than or equal to the Actual Mechanical Advantage (IMA ≥ AMA). This is because AMA accounts for real-world factors like friction and inefficiencies, which reduce the mechanical advantage. Mechanical QCSH Robotics II Mechanical Advantage 1. A worker uses a wheelbarrow (a second-class lever) to lift and transport a load. The load weighs 280 N and is located 0.5 meters from the fulcrum. The worker applies effort at a point 2 meters from the fulcrum. a. What is the Ideal Mechanical Advantage (IMA) of the wheelbarrow? b. If the worker applies an effort force of 80 N, what is the Actual Mechanical Advantage (AMA)? c. What is the efficiency of the wheelbarrow? Mechanical QCSH Robotics II Mechanical Advantage 1. A worker uses a wheelbarrow (a second-class lever) to lift and transport a load. The load weighs 280 N and is located 0.5 meters from the fulcrum. The worker applies effort at a point 2 meters from the fulcrum. a. What is the Ideal Mechanical Advantage (IMA) of the wheelbarrow? Mechanical QCSH Robotics II Mechanical Advantage 1. A worker uses a wheelbarrow (a second-class lever) to lift and transport a load. The load weighs 280 N and is located 0.5 meters from the fulcrum. The worker applies effort at a point 2 meters from the fulcrum. b. If the worker applies an effort force of 80 N, what is the Actual Mechanical Advantage (AMA)? Mechanical QCSH Robotics II Mechanical Advantage 1. A worker uses a wheelbarrow (a second-class lever) to lift and transport a load. The load weighs 280 N and is located 0.5 meters from the fulcrum. The worker applies effort at a point 2 meters from the fulcrum. c. What is the efficiency of the wheelbarrow? EFFICIENCY? Mechanical QCSH Robotics II Mechanical Advantage Efficiency in the context of machines is a measure of how effectively a machine converts the input work (or energy) into useful output work. It is expressed as a percentage and indicates how much of the energy or work put into a machine is used for its intended purpose, with the rest often lost to factors like friction or heat. Mechanical QCSH Robotics II Mechanical Advantage 1. A worker uses a wheelbarrow (a second-class lever) to lift and transport a load. The load weighs 280 N and is located 0.5 meters from the fulcrum. The worker applies effort at a point 2 meters from the fulcrum. c. What is the efficiency of the wheelbarrow? Mechanical QCSH Robotics II Mechanical Advantage 2. A mechanic uses a car jack (a second-class lever) to lift a 770 N car. The load (car) is placed 0.3 meters from the fulcrum, while the mechanic applies an effort force at a distance of 2.1 meters from the fulcrum. a. What is the Ideal Mechanical Advantage (IMA) of the car jack? b. If the mechanic applies an effort force of 140 N, what is the Actual Mechanical Advantage (AMA)? c. What is the efficiency of the car jack? Mechanical QCSH Robotics II Mechanical Advantage 3. Calculate AMA, IMA, and efficiency of the machine. Mechanical QCSH Robotics II Seatwork 4: Mechanical Advantage Two students are testing two different machines to lift the same 500 N load using the same input force of 200 N. Each machine has different mechanical advantages, and you need to determine which machine is more efficient. Machine 1: The output force is 500 N. The input distance is 6 meters. The output distance is 2 meters. Machine 2: The output force is 500 N. The input distance is 6.5 meters. The output distance is 2.5 meters. Mechanical QCSH Robotics II Mechanical Advantage Mechanical QCSH Robotics II  The Lever Mechanical QCSH Robotics II Objectives: At the end of the session, you are expected to: a. Classify types of levers, identify components, and apply the principle of moments. b. Build lever models and calculate mechanical advantage. c. Appreciate the role of levers in simplifying work and real-life applications. Mechanical QCSH Robotics II The Lever A lever is a simple machine consisting of a rigid bar that rotates about a fixed point called the fulcrum. It operates on the principle of moments to amplify force, making it easier to perform tasks like lifting or moving loads. The primary function of a lever is to transfer and amplify mechanical energy. Mechanical QCSH Robotics II The Lever A lever is a mechanism that can be used to exert a large force over a small distance at one end of the lever by exerting a small force over a greater distance at the other end. dl de Fe Effort Force Fl Load Force Mechanical QCSH Robotics II Core Components Fulcrum: The fixed pivot point about which the lever rotates. Load (Fl): The resistance force that needs to be overcome. Effort (Fe): The applied input force to move the load. Load Arm (dl): The distance from the fulcrum to the point where the load is applied. Effort Arm (de): The distance from the fulcrum to the point where effort is applied. Mechanical QCSH Robotics II Core Components Mechanical QCSH Robotics II  Principle of Moments Mechanical QCSH Robotics II Principle of Moments A moment is the measure of the turning effect or rotational force produced by a force acting at a distance from a pivot point or axis of rotation. Moments describe how a force causes an object to rotate about a specific point. The moment of a force (𝑀) is the product of the magnitude of the force (𝐹) and the perpendicular distance (𝑑) from the line of action of the force to the pivot point. Mechanical QCSH Robotics II Principle of Moments The Principle of Moments states that for a system to be in equilibrium, the sum of the clockwise moments about a point must be equal to the sum of the counterclockwise moments about the same point. In mathematical terms: Mechanical QCSH Robotics II Principle of Moments The principle of levers is governed by the Law of Moments, which states: Mechanical QCSH Robotics II Principle of Moments Gravity = 10m/s2 20 kg ? kg What is the minimum force required to lift the crate into balance using the lever? Mechanical QCSH Robotics II Principle of Moments Gravity = 10m/s2 4m 1m An 80-kg bear balances the cub on a lever as shown. What is the approximate mass of the cub? What, approximately, is the magnitude of the Mechanical QCSH downward force exerted on the fulcrum? Robotics II Types of Levers Levers are classified into three categories based on the relative positions of the fulcrum, effort, and load: 1st Class 2nd Class 3rd Class Note: Motion of load is upward Mechanical QCSH Robotics II Types of Levers First-Class Lever Fulcrum is positioned between the effort and the load. Can provide a mechanical advantage or speed advantage depending on the arm lengths. Examples: Effort ✔ Seesaw Load ✔ Crowbar ✔ Scissors 1 st Class Fulcrum Mechanical QCSH Robotics II Types of Levers Problem 1: Lifting a Rock with a Crowbar A worker uses a crowbar to lift a 300 N rock. The fulcrum is positioned 0.3 m from the rock, and the worker applies force 1.2 m from the fulcrum. a. What is the mechanical advantage of the crowbar? b. How much effort force must the worker apply to lift the rock? Mechanical QCSH Robotics II Problem 1: Lifting a Rock with a Crowbar A worker uses a crowbar to lift a 300 N rock. The fulcrum is positioned 0.3 m from the rock, and the worker applies force 1.2 m from the fulcrum. a. What is the mechanical advantage of the crowbar? b. How much effort force must the worker apply to lift the rock? 300 N 1.2 m 0.3 m Types of Levers Problem 2: Scissors Cutting Paper A person uses scissors to cut paper. The fulcrum (pivot point) is located 2 cm from the cutting edge of the blades, and the person applies force 6 cm from the fulcrum. a. What is the mechanical advantage of the scissors? b. If the paper requires a cutting force of 15 N, how much effort force must the person apply? Mechanical QCSH Robotics II Problem 2: Scissors Cutting Paper A person uses scissors to cut paper. The fulcrum (pivot point) is located 2 cm from the cutting edge of the blades, and the person applies force 6 cm from the fulcrum. a. What is the mechanical advantage of the scissors? b. If the paper requires a cutting force of 15 N, how much effort force must the person apply? 15 N 6 cm 2 cm Types of Levers Second-Class Lever Load is positioned between the fulcrum and the effort. Always provides a mechanical advantage because the effort arm is longer than the load arm. Examples: Effort Wheelbarrow Load Nutcracker Bottle opener nd 2 Class Fulcrum Mechanical QCSH Robotics II Types of Levers Problem 3: Moving a Rock A gardener uses a wheelbarrow as a lever to lift a 100 kg rock. The rock is placed 0.5 m from the wheel (the fulcrum), and the gardener applies force to the handles 1.5 m away from the wheel. a. What is the mechanical advantage of the lever? b. If the gardener applies a force of 400 N, will they be able to lift the rock? Mechanical QCSH Robotics II Problem 3: Moving a Rock A gardener uses a wheelbarrow as a lever to lift a 100 kg rock. The rock is placed 0.5 m from the wheel (the fulcrum), and the gardener applies force to the handles 1.5 m away from the wheel. a. What is the mechanical advantage of the lever? b. If the gardener applies a force of 400 N, will they be able to lift the rock? 100 kg 0.5 m 1.5 m Types of Levers Problem 4: Carrying Supplies A delivery worker uses a dolly to carry a box weighing 200 N. The box is placed 0.8 m from the fulcrum, and the worker applies effort 2.4 m from the fulcrum. a. Calculate the mechanical advantage of the dolly. b. What effort force does the worker need to apply to lift the box? Mechanical QCSH Robotics II Problem 4: Carrying Supplies A delivery worker uses a dolly to carry a box weighing 200 N. The box is placed 0.8 m from the fulcrum, and the worker applies effort 2.4 m from the fulcrum. a. Calculate the mechanical advantage of the dolly. b. What effort force does the worker need to apply to lift the box? 200 N 0.8 m 2.4 m Types of Levers Problem 5: Opening a Paint Can A painter uses a small pry bar to lift the lid of a paint can. The fulcrum is placed 2 cm from the edge of the lid, and the painter applies force 6 cm from the fulcrum. a. What is the mechanical advantage of the pry bar? b. If the force required to lift the lid is 30 N, how much effort force must the painter apply? Mechanical QCSH Robotics II Problem 5: Opening a Paint Can A painter uses a small pry bar to lift the lid of a paint can. The fulcrum is placed 2 cm from the edge of the lid, and the painter applies force 5 cm from the fulcrum. a. What is the mechanical advantage of the pry bar? b. If the force required to lift the lid is 30 N, how much effort force must the painter apply? 200 N 2 cm 6 cm Types of Levers Third-Class Lever Effort is applied between the fulcrum and the load. Provides a speed advantage but requires more effort than the load. Examples: ✔ Tweezers Load Effort ✔ Fishing rod ✔ Broom rd 3 Class Fulcrum Mechanical QCSH Robotics II Types of Levers Problem 6: Fishing Rod A person uses a fishing rod to lift a fish weighing 50 N. The effort is applied 0.2 m from the fulcrum, and the fish is located 1.2 m from the fulcrum. a. What is the mechanical advantage of the fishing rod? b. How much effort force does the person need to apply to lift the fish? Mechanical QCSH Robotics II Problem 6: Fishing Rod A person uses a fishing rod to lift a fish weighing 50 N. The effort is applied 0.2 m from the fulcrum, and the fish is located 1.2 m from the fulcrum. a. What is the mechanical advantage of the fishing rod? b. How much effort force does the person need to apply to lift the fish? 50 N 0.2 m 1.2m Types of Levers Problem 7: Baseball Bat Swing A player swings a baseball bat, applying force 0.3 m from the fulcrum (near their hands). The bat hits the ball 1.5 m away from the fulcrum. a. Calculate the mechanical advantage of the bat. b. If the player applies 80 N of force, what is the force exerted on the ball? Mechanical QCSH Robotics II Problem 7: Baseball Bat Swing A player swings a baseball bat, applying force 0.3 m from the fulcrum (near their hands). The bat hits the ball 1.5 m away from the fulcrum. a. Calculate the mechanical advantage of the bat. b. If the player applies 80 N of force, what is the force exerted on the ball? 80 N 0.3 m 1.5m Types of Levers Problem 8: Broom Sweeping A person sweeps the floor with a broom. The effort is applied 0.5 m from the top of the broomstick (fulcrum), and the sweeping end is 1.5 m from the fulcrum. a. What is the mechanical advantage of the broom? b. If the person applies a force of 30 N, what force is exerted at the sweeping end? Mechanical QCSH Robotics II Problem 8: Broom Sweeping A person sweeps the floor with a broom. The effort is applied 0.5 m from the top of the broomstick (fulcrum), and the sweeping end is 1.5 m from the fulcrum. a. What is the mechanical advantage of the broom? b. If the person applies a force of 30 N, what force is exerted at the sweeping end? 30 N 0.3 m 1.5m Summary Levers are versatile tools that have been used for centuries to make tasks easier. Understanding the principles of levers helps in designing tools and machinery for various applications, from everyday tools to advanced engineering systems. Mechanical QCSH Robotics II Seatwork no. 5 1. A carpenter uses a lever arm to lift a heavy block weighing 500 N. The fulcrum is placed 1.5 m from the load, and the carpenter applies effort 4.5 m from the fulcrum on the opposite side. a. What is the mechanical advantage of the lever arm? b. How much effort force must the carpenter apply to lift the block? 2. A person uses tweezers to lift a small object. The effort is applied 2 cm from the fulcrum, and the object is located 4 cm from the fulcrum. a. What is the mechanical advantage of the tweezers? b. If the person applies a force of 10 N, what force is exerted on the object? 3. A seesaw is modified to act as a second-class lever to lift a heavy object. The load is placed 2 m from the fulcrum, and the person applies effort 6 m from the fulcrum. a. What is the mechanical advantage of the system? b. If the object weighs 600 N, what force must the person apply to lift it? Mechanical QCSH Robotics II 4m 1m  1.8 m 245 N 400 N 1.2 m Actuator  The Pulley Mechanical QCSH Robotics II Objectives: At the end of the session, you are expected to: a. explain the purpose of pulleys and identify the components of a pulley system. b. distinguish between fixed, movable, and compound pulleys and describe how each type affects the effort required to lift a load. c. calculate the mechanical advantage of pulley systems in ideal and real-world scenarios, demonstrating how pulleys reduce the effort needed to lift objects. Mechanical QCSH Robotics II Pulley and Its Mechanical Advantage A pulley is a simple machine consisting of a wheel with a groove along its edge, through which a rope, belt, or chain can pass. It is used to change the direction of force and, in some configurations, reduce the amount of force needed to lift or move a load. Pulleys are a fundamental tool in mechanical systems and are widely used in lifting and rigging operations. Mechanical QCSH Robotics II Components of a Pulley Wheel/Groove: The circular component with a groove that guides the rope or cable. Axle: The fixed point or shaft about which the wheel rotates. Rope/Belt/Chain: The medium that transmits force across the pulley. Load: The object being lifted or moved. Effort: The force applied to move the load. Mechanical QCSH Robotics II Components of a Pulley Wheel/Groove Rope/Belt/ Axle Chain Load Effort Load Mechanical QCSH Robotics II Types of Pulleys Fixed Pulley In this pulley, the wheel is fixed to a hard structure while the rope is loose. It does not allow any redirection of force. So instead of lifting an object, the object can be pulled using this pulley. Mechanical QCSH Robotics II Types of Pulleys Moving Pulley Here, the pulley’s wheel is not linked to any surface but the rope is linked to a stationary surface. A heavy load is attached to the wheel rather to the rope and when the rope is pulled, the wheel can be seen sliding up the rope along with the load. This needs less work compared to lifting the load directlyx. Mechanical QCSH Robotics II Types of Pulleys Compound Pulley It has both stationary and movable pulley. Here the load is kept on the wheel of the movable pulley which again is connected to the rope of a fixed pulley. Using this type of pulley, redirection of both the force applied and the total workload is possible. Mechanical QCSH Robotics II Types of Pulleys Block and Tackle Pulley It can reduce the effort required to move a heavy object. It has several movable and fixed pulleys arranged in parallel with each other in such a way that fixed ones are with fixed and movable are with the movables. An each pair is linked with another pair. Mechanical QCSH Robotics II Efficiency and Real-World Factors In real systems, the actual mechanical advantage is less than the ideal due to: Friction: Between the rope and the pulley. Deformation: Of the rope or pulley under load. Rope stretch: Particularly in elastic materials. Mechanical QCSH Robotics II Applications of Pulleys Construction: Lifting heavy materials like steel beams. Transportation: Elevators and cable cars. Maritime Industry: Rigging and cargo loading on ships. Daily Life: Clotheslines and window blinds. Mechanical QCSH Robotics II Mechanical Advantage of a Pulley The mechanical advantage (MA) of a pulley system is the factor by which the force exerted by the user is multiplied. It is calculated as: Alternatively, for ideal (frictionless) pulleys: Mechanical QCSH Robotics II Load Load Load Load Load Load Load Load  Pulleys are a testament to the ingenuity of simple machines, enabling humans to perform tasks that would otherwise require far greater effort. Their mechanical advantage and versatility make them an indispensable tool across various industries and applications. Mechanical QCSH Robotics II Seatwork no. 6 Determine the forces acting in the given pulley system. Load Load Mechanical QCSH Robotics II Load Load Load Load Load Load