Mechanical Advantage & Simple Machines Physics 5 th Six Weeks
And now, for an appetizer: Bill Nye and using Mechanical Advantage
Mechanical Advantage A machine is something that makes doing work easier A machine s mechanical advantage is the number of times a machine increases the force delivered to it by a user. Or put another way MA is a way of describing how much a machine reduces the force required to do a particular task by a user. Mechanical Advantage is also known as Leverage Finding the ratio of output force to input force gives you the mechanical advantage of a machine. Effort (aka Effort Force or Input Force ) is the force supplied by the user. Resistance (aka Resistance Force or Output Force ) the force supplied by a machine Mechanical advantage is unit less MA = RF/EF
Practice Problems 1. Calculate the mechanical advantage of a machine that has an input force of 15 N and an output force of 60 N. MA = RF/EF MA = 60 N / 15 N MA = 4 2. Suppose that with a pulley system, you need to exert a force of 1,400 N to lift a heavy object. But without the pulley system, you need to exert 4,200 N to lift the object. What is the mechanical advantage of the pulley system? MA = RF/EF MA = 4200 N / 1400 N MA = 3 3. A child makes a ramp to push his toy dump truck up to his sandbox. If he uses 5.0 N of force to push the 12 N truck up the ramp, what is the mechanical advantage of his ramp? MA = RF/EF MA = 12 N / 5.0 N MA = 2.4
Mechanical Advantage Effort Distance is the distance over which the user applies force (also known as the input distance) Resistance Distance is the distance over which the machine applies force. (also known as the output distance) If you compare the effort distance to the resistance distance, you can find the advantage of using a machine.
Practice Problems 1. You got roped into helping your parents' friend move. You are loading some pretty heavy boxes, but luckily they have a ramp on the back of the truck. The truck is 1.5 meters of the ground and the ramp is 6.0 meters long. What is the MA of this ramp? MA = ED/RD MA = 6.0 m / 1.5 m MA = 4.0 2. A lever used to lift a heavy box has an input arm of 4 meters and an output arm of 0.8 meters. What is the mechanical advantage of the lever? MA = ED/RD MA = 4 m / 0.8 m MA = 5
Circle Diagrams for the Mechanical Advantage formulas RF ED MA EF MA RD MA = Mechanical Advantage (unit less) RF = Resistance Force (force the machine puts out), aka the Load or the Output Force (in Newtons) EF = Effort Force (force put into the machine), aka the Effort or the Input Force (in Newtons) ED = Distance Effort Force is applied (in meters) RD = Distance Resistance Force is applied (in meters)
Practice Problems 1. A ramp with a mechanical advantage of 6 is used to move a 36- newton load. What input force is needed to push the load up the ramp? EF = RF/MA EF = 36 N / 6 EF = 6.0 N 2. Gina wheels her wheelchair up a ramp using a force of 80 N. If the ramp has a mechanical advantage of 7 what is the output force (in Newtons)? RF = MA x EF RF = 7 x 80 N RF = 560 N
Practice Problems 1. A lever with an input arm of 2 meters has a mechanical advantage of 4. What is the output arm s length? RD = ED/MA RD = 2 m / 4 RD = 0.5 m 2. A lever with an output arm of 0.8 meter has a mechanical advantage of 6. What is the length of the input arm? ED = MA x RD ED = 6 x 0.8 m ED = 4.8 m
Introduction A simple machine is a mechanical device that changes the direction or magnitude of a force in only one movement. In general, they can be defined as the simplest mechanisms that use mechanical advantage (also called leverage) to multiply force. A simple machine uses a single applied force to do work against a single load force. Ignoring friction losses, the work done on the load is equal to the work done by the applied force. They can be used to increase the amount of the output force, at the cost of a proportional decrease in the distance moved by the load. The ratio of the output to the input force is called the mechanical advantage.
Introduction Simple Machine a machine that does work in only one movement. There are 6 types of Simple Machine: the lever, the pulley, the wheel and axle, the inclined plane, the screw, and the wedge. They are the elementary "building blocks" of which all more complicated machines (sometimes called "compound machines" to emphasize that they are combinations of the simpler building blocks) are composed. For example, wheels, levers, and pulleys are all used in the mechanism of a bicycle.
History Galileo Galilei Archimedes The idea of a "simple machine" originated with the Greek philosopher and scientist Archimedes around the 3rd century BC He discovered the principle of mechanical advantage The complete theory of simple machines was worked out by Italian scientist Galileo Galilei in 1600 in Le Meccaniche ("On Mechanics"). He was the first to understand that simple machines do not create energy, only transform it 12
Introduction Simple Machine a machine that does work in only one movement. There are 6 types of Simple Machine: the lever, the pulley, the wheel and axle, the inclined plane, the screw, and the wedge. Remember - Mechanical Advantage The ratio of output force to input force, or the number of times that a machine multiplies the effort force. The general formula for Mechanical Advantage is: MA = F o / F i or MA = ED/RD
The Mighty Lever! 14
Levers Definition a bar that is free to pivot or turn on a fixed point. The fixed point on the lever is called the fulcrum. The distance from the fulcrum to where the Effort Force is applied is called the Effort Arm. The distance from the fulcrum to where the Resistance Force is applied is called the Resistance Arm To find the MA of a lever: A) divide the output force by the input force, or B) divide the length of the resistance arm by the length of the effort arm.
1 st Class Lever In a 1 st Class Lever, the fulcrum is located between the Effort Force and the Resistance Force. Examples include, seesaw, crowbar
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Fulcrum is between EF (effort) and RF (load) Effort moves farther than Resistance. Multiplies EF and changes its direction 18
2 nd Class Lever In a 2 nd Class Lever, the load is between the fulcrum and the Effort Force. Examples: wheel barrow, ankle joint
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RF (load) is between fulcrum and EF Effort moves farther than Resistance. Multiplies EF, but does not change its direction 21
3 rd Class Lever In a 3 rd Class Lever, the Effort Force is located between the Resistance Force and the fulcrum. Many pieces of sports equipment are 3 rd class levers. A 3 rd class lever can t multiply the force because the Effort Arm is always shorter than the Resistance Arm. They do however increase the distance over which the force is applied. Examples: shovel, elbow and forearm, baseball bat
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EF is between fulcrum and RF (load) Does not multiply force Resistance moves farther than Effort. Multiplies the distance the effort force travels 24
Fixed Pulleys A pulley is a grooved wheel with a rope, chain, or cable running along the groove. There are 3 types of pulley systems. Fixed Pulley is a stationary, modified 1 st Class Lever with the axle as the fulcrum. A Fixed Pulley can only change the direction of the force. MA = 1
Movable Pulleys In a Movable Pulley System, one end of the rope or chain is fixed, and the wheel is free to move. The Movable Pulley System divides the input force by half MA = 2
Block and Tackle Pulley System. A Block and Tackle Pulley System is a collection of several fixed and movable pulleys. In a block and tackle pulley system, the MA = the number of pulleys in the system. Example: if there were 5 pulleys in the block and tackle pulley system, then MA = 5
Inclined Plane An inclined plane is an even sloping surface. The inclined plane makes it easier to move a weight from a lower to higher elevation. 30
Inclined Plane The mechanical advantage of an inclined plane is equal to the length of the slope divided by the height of the inclined plane. While the inclined plane produces a mechanical advantage, it does so by increasing the distance through which the force must move. 31
The Wedge Definition An inclined plane with 1 or 2 sloping sides. a modification of the inclined plane, the difference between and inclined plane and a wedge is the position of effort Wedges can change the direction of effort force. A double wedge has less MA than a single wedge as it is 2x thicker.
The Wedge (and yes force is in Newtons, but it s a free clip just remember F in Newtons = mass in kg x g) 33
Screw The screw is also a modified version of the inclined plane. While this may be somewhat difficult to visualize, it may help to think of the threads of the screw as a type of circular ramp (or inclined plane). A screw conveyor (aka an Archimedes Screw ) uses a rotating helical screw blade to move bulk materials. 34
MA of an screw can be calculated by dividing the number of turns per inch. 35
Using an Archimedes Screw to move Cheerios
Archimedes Screw Ball Lift
Legos and an Archimedes Screw
Wheel and Axle Definition a machine consisting of two wheels of different sizes that rotate together. The larger wheel has the EF exerted upon it, while the smaller wheel (the axle) usually exerts the RF. (exp. Bicycle tire, pencil sharpener, gears)
The mechanical advantage of a wheel and axle is determined by: Wheel Radius MA = Axle Radius A wheel and axle can be used to alter force (such as amplifying the operator s input force to allow heavier objects to be picked up than without the machine). A wheel and axle can also be use to reduce friction such as the wheels on a skateboard which makes doing work easier.
Wheel and axle, etc. 41
Efficiency of Machines So far, you have learned that the work you put into a machine is exactly equal to the work done by the machine. In an ideal situation, this equation is true. The efficiency of an ideal machine is always 100% In real situations, however, the output work is always less than the input work due to friction.
Friction and Efficiency If you have ever tried to cut something with scissors that barely open and close, you know that a large part of your work is wasted overcoming the tightness, or friction, between the parts of the scissors. In every machine, some work is wasted overcoming the force of friction. The less friction there is, the closer the output work is to the input work.
Calculating Efficiency To calculate the efficiency of a machine, divide the output work by the input work and multiply the result by 100 percent. This is summarized by the following formula. (remember from your previous use of the formula if you get more than 100% the values are in the wrong order!)
Calculating Efficiency You do 20 J of work while using a hammer. The hammer does 18 J of work on a nail. What is the efficiency of the hammer? 90% (2) Calculating Efficiency Suppose you left your lawn mower outdoors all winter. Now it s rusty. Of your 250,000 J of work, only 100,000 J go to cutting the lawn. What is the efficiency of the lawn mower now? 40%