Practice #3—Pulleys Mr. Burleson geaux15@hotmail.com Machines

Agenda Review What are pulleys IMA for different types of pulleys Rove to Advantage/Disadvantage Simple Machines Practical Homework

What is Force? Force is any influence that causes an object to undergo a certain change, either concerning its movement, direction, or geometrical construction. In other words, a force can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or a flexible object to deform, or both. Force is measured in the SI unit of Newtons and represented by the symbol F. Force can also be described by intuitive concepts such as a push or a pull. A force has both magnitude and direction, making it a vector quantity.

What is the most important formula in all of Physics? Sir Issac Newton created three main laws of Physics. The second law is the net force acting upon an object is equal to the change of momentum or for a static mass, force equals mass times acceleration The arrow indicates the direction of the acceleration and the direction of the force The magnitude is the size/number The direction with the magnitude makes it a vector  

Basics of Simple Machines Lever Inclined Plane Wheel and Axle Wedge Pulley Screw (not included in Machines [B])

What is a pulley? A pulley is a wheel on an axle that is designed to support movement of a cable or belt along its circumference. Pulleys are used in a variety of ways to lift loads, apply forces, and to transmit power. Also called a block, sheave, or drum and may have a groove between two flanges around its circumference. The drive element of a pulley system can be a rope, cable, belt, or chain that runs over the pulley inside the groove.

How does a pulley work? Assume the following: The lines/rope involved easily wrap around the pulleys and do not expand The force (tension) at one end of the lines/rope is the same in the opposite direction in the rest of the rope If you have multiple lines holding up the same load, each line takes an equal amount of weight (tension) If the pulley is static, not moving, then all the forces on a pulley are equal to zero.

Ideal Pulley Assumes the lines do not stretch or expand No friction in the lines or the pulleys Pulleys are weightless Efficiency η = 1

Types of Pulleys Three major types Fixed: A fixed pulley has an axle mounted in bearings attached to a supporting structure. A fixed pulley changes the direction of the force on a rope or belt that moves along its circumference. Mechanical advantage is gained by combining a fixed pulley with a movable pulley or another fixed pulley of a different diameter. Movable: A movable pulley has an axle in a movable block. A single movable pulley is supported by two parts of the same rope and has a mechanical advantage of two. Compound: A combination of fixed and a movable pulleys forms a block and tackle. A block and tackle can have several pulleys mounted on the fixed and moving axles, further increasing the mechanical advantage.

Named Pulleys IMA 2 3 4 5 6

Single Pulley IMA = 1 or 2 With IMA of 1 often used to change direction of Effort versus Tension With IMA of 2 often used to lift up a heavier load

Rove to Advantage/Disadvantage Rove to Advantage means that the Effort force is in “approximately” the same direction of the Weight/Load Force Lifting a weight from above Rove to Disadvantage means that the Effort force is in “approximately” the opposite direction of the Weight/Load Force Pulling a weight up from below Note that you can change the IMA of a pulley system by changing the Rove Gun Tackle “Rove to Adv” IMA = 3 Gun Tackle “Rove to Disadv” IMA = 2 Gun Tackle "rove to advantage" has the rope attached to the moving pulley. IMA = 3 Luff tackle adds a fixed pulley "rove to disadvantage." IMA = 3

Sailing Terms Block and Tackle Single or multiple pulleys in sailing are called Blocks. One or a number of sheaves are enclosed in an assembly between cheeks or chocks. A Block is fixed to the end of a line, to a spar, or to a surface. A line (rope) is reeved through the sheaves, and maybe through one or more matching blocks at some far end, to make up a tackle. Other Sailing Terms A block and tackle is a system of two or more pulleys with a rope or cable threaded between them, usually used to lift or pull heavy loads The Purchase of a tackle refers to its IMA A Ratchet Block turns freely when a line is pulled in one direction but does not turn the other direction, although the line may slip past the sheave When a pulley cannot raise the load any more because the cheeks of the two blocks are against each other they are “Chock a’ Block”

Pulleys Can be Drawn Separate The two pulleys below are the same, but the Sheaves are drawn separate =

How to solve a pulley problem? Start with the Load Split the forces with all the supporting lines Use tension to solve for the upper forces Use the last Sheave to translate the Effort

Example #1 Start with the Load of 100 N down The one line holding up the load is 100N pointing up The one lines has the tension causing the 100 N force on the top fixed pulley pulling down The tension from the furthest right line transforms through the top fixed pulley, causing a 100 N force on the Effort Line pointing down To keep it all from falling down, the top fixed pulley supports 200 N including the one line holding the Load and the one line holding the Effort

Example #2 Gun Tackle Start with the Load of 100 N down The two lines holding up each support half the weight or 50 N each pointing up The two lines then have the tension causing the 50 N force on the top fixed pulley pulling down The tension from the furthest right line transforms through the top fixed pulley, causing a 50 N force on the Effort Line pointing down To keep it all from falling down, the top fixed pulley supports 150 N including the two lines holding the Load and the one line holding the Effort

Example #3 Double Tackle Start with the Load of 100 N down The four lines holding up each support half the weight or 25 N each pointing up The four lines then have the tension causing the 100 N force on the top fixed pulley pulling down The tension from the furthest right line transforms through the top fixed pulley, causing a 25 N force on the Effort Line pointing down To keep it all from falling down, the top fixed pulley supports 125 N including the four lines holding the Load and the one line holding the Effort

Detailed Drawing of the Double Tackle Problem

Examples of Multiple Pulley Systems

Pulleys linked by a circular chain or belt Below is a pulley and belt system, which operates like a Wheel and Axle, but is classified a pulley system Pulleys have different axles Motion is circular/angular not linear The IMA is dependent upon the ratio of the wheels/pulleys versus the number of lines connecting One wheel/pulley is the driver and one is the driven

Ideal Drive Pulley System No friction around the axles No slippage of the belt or chain No expansion or stretching of the belt or chain

In Practice Quiz Draw the weight and tension lines (please note on the right hand side it is attached to a fixed position) Which color is Load and which color is Effort? What is the IMA? Is this Rove to Advantage or Rove to Disadvantage?

In Practice Quiz #2 What type of Named Pulley are each? What is the IMA of each? Other than the IMA, what is the difference?

Practical Get a small load, a pulley and string For the pulley, you can either use a pulley or something that a piece of string or rope can easy go over (like a pencil or other rod)--this would be like throwing a rope over a branch of a tree to use the branch as the “pulley” See if you can configure an IMA of 1, 2 or higher using the string Does the higher IMA take more or less force/tension? Does the higher IMA require you to pull more/less distance of string/rope to move the load the same distance?

Homework #3 Pulleys If you haven’t started, build your lever measurement device Solve the tension in each line, force on each pulley, Effort required, and IMA of each pulley system as shown on the next few slides Do Homework Generator Pulley Levels 1, 2, and 3

Homework (cont)

Homework (cont) Assume Load = 300N

Homework (cont) A = D = F = H = J = 50N Solve for B, C, E, G, and I

Homework (cont) Crate weights 200N Gauge reads 100N