Mechanical Advantage And how it applies to simple machines

Mechanical Advantage (n): A ratio between forces or distances input into a machine and the output of forces or distances.

Need more Force? Usa a machine!

Need more Distance? Usa a machine!

Machines for daaaaaaaays! There are seven types of simple machines. (Most people think there’s six, but there are actually seven.) These machines can create mechanical advantage for force or distance. Each one allows you to put a small force in and get a large force out, or put a small distance in and get a small distance out. But it comes at a cost. Ramp Wedge Screw Pulley Lever Wheel and Axle Hydraulic Press

Ramp Long ramp Less force - more distance Short ramp More force - less distance Movers are pushing a fridge into the moving van. The van bed is 0.7 meters from the ground. The fridge weighs 500 kgs. Even though the two movers are burly men from Sweden, there is no way they can lift 500 kgs. The hardest they can push is 600 N. Describe how they can use a ramp to get the fridge in the van.

Ramp Simple machines can produce EITHER more force OR more distance, but not both. WORK IN = WORK OUT Force and Distance come at the cost of one another. If the movers can’t push very hard, they can use a ramp to get the job done, but they must push a longer distance. Let’s look at the math. W i = W o W i = Fd W i = 600(d) 3,430 = 600(d) d = 5.72m The ramp must be at least 5.72 m long. The “Work” way W i = W o W o = Fh W o = mgh W 0 = 500(9.8)(0.7) W 0 = 3,430 J

Ramp If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance The ramp must be at least 5.72 m long. The “Mechanical Advantage” way

Wedge Long wedge Less force - more distance Short wedge More force - less distance If a dull axe has a head that is 0.3 m long and is honed to an edge of 3˚, and can split wood with only 120 N of force. The old axe in the garage of the same model hasn’t been sharpened in a while and has an edge 12˚ wide. How much force does it need to chop logs?

Wedge If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance It must use N of force The “Mechanical Advantage” way

Screw Long screw Less force - more distance Short screw More force - less distance One screw of radius m has 200 turns along its length. The screw is 0.04 m long If only 12 Newtons of force are required turn the screw, how much force does it actually drive itself into the wall with?

Screw If you put in less force, you must go through a larger number of turns. If you put in more force, need only go a few number of turns. It drives into the wall with 2,513 N. The “Mechanical Advantage” way

Lever In opening a can of pain, you pry the top with a screwdriver. The tip of the screwdriver is m from the edge of the can around which it turns. The rest of the screwdriver extends 0.03 m past the edge of the paint can. If you push down with 10 N of force, how much is applied to the paint lid? Long lever Less force - more distance Short lever More force - less distance

Lever If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance It pries the lid with 100 N of force. The “Mechanical Advantage” way

Wheel and Axle A biker is going for speed in a race and switches to his highest gear ratio. The primary gear has a radius of 0.25 m. The secondary gear has a radius of 0.05 m. If the secondary gear pushes the wheels with 50 N of force, how much force must be put into the first gear? Large gear Less force - more distance small gear More force - less distance

Wheel and Axle If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance 250 N of force must be put into the first gear. The “Mechanical Advantage” way

Pulley A crane has a pulley system where the load being lifted is supported by 6 weight bearing cables through. If the crane’s motor pulls produces 300 N of force, what is the maximum weight it can lift? Pull one line Less force, more distance Pull multiple lines More force, less distance

Wheel and Axle If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance The crane can lift a maximum load of 1800 N. The “Mechanical Advantage” way

Hydraulic Press

A hydraulic lift in a car garage says it can lift a maximum of 500,000 N a distance of 3 m in the air. The lifting pistons have a radius of 0.04 m. If the driving piston has a radius of m, how far must they move to lift the car? How much force is required? Small piston Less force - more distance Large piston More force - less distance

Hydraulic Press If you put in less force, you must go a greater distance. If you put in more force, you must go a smaller distance It must push for 1,200 m. The “Mechanical Advantage” way