How Machines Do Work: Advantageous and Efficient Notes

What is a machine? A machine is a device that can be used to perform work easily, or in a more efficient manner.

How do machines make work easier? Does a machine change amount of work? By changing the amount of force you exert, the distance over which you exert your force, or the direction in which you exert the force. NO! A machine does not change the amount of work!

In Summary, 3 Basic things a machine changes are… ForceDistanceDirection

Input Force and Distance Input Force - The effort or force you exert on the machine Input Distance - The distance you move the machine

Output force and Distance Output Force - The force exerted by the machine on the object (also called resistance or the load and always equal the weight if the machine lifts it) Output Distance - The distance the machine moves

Input and Output Work Input force x input distance = input work –Work done by you! (I do input work) Output force x output distance = output work –Work done by the machine! (M, O) Output work can never be greater than input work!

Increasing (multiplying) a Force Input (you) Small force Large distance Output (machine) Large force Small distance Input force less than output force! Examples: Ramp: large ramp distance (input) to lift something up a smaller height (output distance)

Increasing (multiplying) a Distance Input (you) Large force Small distance Output (machine) Small force Large distance Input force more than output force! Input distance less than output distance! Examples: Hockey stick (you move stick small distance, bottom of stick moves large distance to hit puck) Chopstick (you move hands small distance, end of sticks move large distance to pick up food) Bicycle (you move legs small distance, bike moves a larger distance)

FYI: A little something about force and distance Think of force and distance as if they are on a see-saw – when one goes up the other goes down If the machine’s force (output) is less than your force (input), then the output distance needs to be more than the input distance If the machine’s force (output) is more than your force (input), then the output distance needs to be less than the input distance

Changing Direction of Work If a machine only changes direction: Input and output force are the same, input and output distance are the same Examples: –Weight machine: you pull down, weight moves up –Sailboats: you pull rope down, sail goes up (this is a lot easier than standing on the top of the mast and pulling the sail up!)

Mechanical Advantage A machine’s mechanical advantage is the number of times a force exerted on a machine is multiplied by the machine. Mechanical Advantage = Output Force Input Force Input Force No units for MA!

Let’s open a can with a can opener. If you exert 10 Newtons on the opener, and the opener exerts a force of 30 Newtons on the can, then what is the mechanical advantage? MA = output F / input F Mechanical Advantage = 30N 10N 10N Mechanical Advantage = 3 The machine increased the force exerted (times 3!), so it must have decreased the distance

Another Example The input force on a machine is 20 N and the output force is 10 N. What is the MA? MA = output F / input F MA = 10 N / 20 N MA = 0.5 Machine decreased force (divided by 2), but must have increased distance

What is happening to the MA? If MA is over 1: Force is multiplied! (output force more than input, output distance is less) If MA is less than 1 Distance is multiplied! (output force less than input, so output distance is more) If MA = 1 Machine only changes direction – force and distance are the same for input and output

Efficiency Ideally: the input work will equal the output work This does not occur in the real world due to friction (some work needs to be used to overcome the friction) Efficiency: compares output work to input work –Always a percentage –Higher the percentage more efficient the machine

To Calculate Efficiency Efficiency = Output work x 100 Input work Input work

Let’s say you cut the lawn with a hand lawn mower. You do 250,000 Joules of work to move the mower. If the work done by the mower in cutting the lawn is 200,000 Joules, what is the efficiency of the lawn mower? Efficiency = 200,000 J X ,000 J 250,000 J Efficiency = 0.8 x 100 Efficiency = 80%

Real and Ideal Machines There is no machine that is perfect; all machines have friction. The efficiency of every machine is less than 100%. ideal mechanical advantage (IMA): The mechanical advantage of a machine without friction (100 % efficient) actual mechanical advantage (AMA): Machine’s measured (real life w/ friction) MA

Summary For both MA and efficiency: out/in MA: use force Efficiency: use work

A little question for you… You are moving a table up to the door of your house. Instead of carrying the table up the front stairs, you use a ramp. You put in 200 N of force to move the 30 kg table. The door is 3 m up from the ground and the ramp is 6 m long. What is the mechanical advantage of the ramp? What is the efficiency of the ramp?

Mechanical Advantage Output F = 30 kg * 9.8 m/s 2 = 294 N (WEIGHT) Input F = 200 N Mechanical Advantage = output F input F input F MA = 294 N / 200 N MA = 1.47

Efficiency Output W = output F x output D 294 N * 3 m = 882 J (use height of ramp as D) Input W = input F x input D 200 N * 6 m = 1200 J (use length of ramp as D – this is how far you move) E = (output W / input W) * 100 Efficiency = 882 J / 1200 J = * 100 = 73.5% efficient

If you were to find the IMA… output W = input W since machine would be 100% efficient So - input work would be 882 J not 1200 J (no friction so no extra work needed) IF = IW / ID – need to find new input force = 882 J / 6 m (882 Nm / 6 m) = 882 J / 6 m (882 Nm / 6 m) = 147 N (new input force) = 147 N (new input force) MA = 294 N / 147 N = 2 = IMA

Another Way to Find this Ideal Mechanical Advantage for a Ramp (only a ramp) Ideal MA = length of ramp height of ramp height of ramp Ideal MA = 6m / 3m = 2 This way is easier!!!

Now make the Magic Triangles for MA & Efficiency.

Mechanical Advantage MA = Mechanical Advantage OF = Output force IF = Input Force IF = Input Force MA = OF/IF (OF ÷ IF) OF = MA x IF IF = OF/MA (OF ÷ MA) IF = OF/MA (OF ÷ MA) MA OF IF

Efficiency OW IW Eff  Eff = Efficiency  OW = Output work  IW = Input work  Eff = OW/IW (OW ÷ IW)  OW = Eff x IW  IW = OW/Eff (OW ÷ Eff)  Note the efficiency in magic triangle is a decimal.