Simple Machines Chana Goodman, Doral Academy Preparatory School, 2011-2012 based on a PowerPoint by M. Hunter
Essential Question How can mechanical advantage be calculated, and used to predict effort and resistance force for levers, pulleys, wheel and axles, and incline planes?
Definition: What is a machine? If you combine two or more simple machines in order to perform a task, you have made a compound machine. A machine is a tool used to make work easier Machines help you move objects! Remember... work = Force * Distance.
And how precisely are these machines going to make work easier for me? Machines make work easier in two ways: 1. They reduce the amount of work you have to do in order to move an object. and/or 2. They change the direction of movement of an object.
What kinds of simple machines are there?
I. Levers
More Definitions! 2 3 1 1. Fulcrum The point around which the lever turns 2. Effort arm This is where you push down 3. Resistance arm: This is where you put the item you want to lift (also called 'the load')
What is mechanical advantage? Mechanical advantage is a ratio that describes the 'efficiency' of the machine
What's the big deal?
You can use a machine's mechanical advantage to predict... 1. Effort Force: How hard you have to push / pull 2. Resistance Force The weight of the load you want to move 1 2 For specific examples of calculating resistance and effort force using mechanical advantage, see the last few slides of this presentation
Calculating Mechanical Advantage of levers MA = LRA / LEA In plain English Excellent question thank you for asking! MA has no unit of measure. MA is simply a ratio, like pi.
Examples! If the resistance arm is 5 cm long, and the effort arm is 100 cm long... What is the mechanical advantage of this lever?
1. Write your formula MA = LRA / LEA 2. Identify variables LRA = 5 cm LEA = 100 cm 3. Plug in the numbers MA = 5 cm / 100 cm 4. Do the math MA = 0.05
Block and Tackle: The block is the pulley the tackle is the rope. Pulleys Pulleys can be fixed. or moveable.
Definitions A fixed pulley: is fastened to a fixed or unmoving place like a wall or ceiling. A moveable pulley is fastened to the load. The load has to move, hence the name moveable.
How do I calculate the MA of this pulley? 1. Write your formula MA = 1 / # pulleys (aka blocks) 2. Identify variables # pulleys (blocks) = 1 3. Plug in the numbers MA = 1 / 1 4. Do the math MA = 1
How do I calculate the MA of this pulley? 1. Write your formula MA = 1 / # pulleys (aka blocks) 2. Identify variables # pulleys (blocks) = 2 3. Plug in the numbers MA = 1 / 2 4. Do the math MA = 0.5
And, how do I calculate the MA of this pulley? 1. Write your formula MA = 1 / # pulleys (aka blocks) 2. Identify variables # pulleys (blocks) = 11 3. Plug in the numbers MA = 1 / 11 4. Do the math MA = 0.09
Don t get mad but There is another way to calculate MA of a pulley.
by dividing 1 (number of parts of rope going to and from the moveable block) One in and One out MA = 1 2 = 0.5 MA = 1 3 = 0.33 Two in and one out to bottom pulley.
The Wheel and Axle Effort Force applied to a large wheel, with radius = r 1 To turn a smaller axle, with radius = r 2
Wheel & Axle: Mechanical Advantage The mechanical advantage is the ratio of the radii of the wheel and axle Which means, mathematically r 1 (radius of axle) MA = ---------------------------- r 2 (radius of wheel)
Example time! What is the mechanical advantage of the screwdriver at the right? 1. Write the formula MA = r 1 / r 2 2. Identify variables Axle radius = 0.3 cm Wheel radius = 1.5 cm 3. Plug in the numbers 0.3/1.5 4. Do the math 0.2
INCLINE PLANE An INCLINE PLANE is a sloping surface The Incline Plane does not MOVE. The plane allows you to use less force over a long distance.
Calculating Mechanical Advantage of Incline Planes Formula MA = HR / LR Length of ramp In plain English Mechanical advantage = height of the ramp / length of the ramp Height of ramp
Example time! Calculate the mechanical advantage of this incline plane. 9 feet 3 feet
9 feet 1. Write your formula MA = HR / LR 2. Identify variables HR = 3 feet LR = 9 feet 3. Plug in the numbers MA = 3 feet / 9 feet 4. Do the math MA = 0.33 3 feet
Even MORE Incline Planes!!!
Now let's calculate the Mechanical Advantage of wedges and screws! Cool your jets, cowboy. She's kidding. You'll learn that next year, in physics. Why you little...
Using mechanical advantage to calculate Effort Force Remember Effort force = how hard you push down Formula EF = MA x RF In plain English How hard do I have to work? = Mechanical advantage x Weight of the load
Example! If you have a lever with MA = 0.05, and you want to lift a load weighing 6000 pounds, How hard do you have to push? (or, how much does the person sitting on the effort arm, have to weigh?)
1. Write your formula EF = MA * RF 2. Identify variables MA = 0.05 RF = 6000 pounds 3. Plug in the numbers EF = 0.05 x 6000 lbs. 4. Do the math you have to push (or weigh) 300 lbs.
Using mechanical advantage to calculate resistance force Remember: Resistance force = the weight of the load you are trying to lift Formula RF = EF / MA In plain English How much can I lift? = How hard I press down / Mechanical advantage
Example time! I want to use this screwdriver to tighten a screw. My hands are tired, and I know that I can only turn the handle with a force of 3 pounds. If pounds of force to turn the screw, are my hands strong enough for the job?
1. Write your formula RF = EF / MA 2. Identify variables MA = 0.2 EF = 3 pounds 3. Plug in the numbers RF = 3 lbs. / 0.2 4. Do the math RF = 15 pounds. Yes, I can do this job, tired hands and all.