Simple Machines - LCHS Physical Science LCHS Main SiteSD271 Main site
Objectives: The learner will...
...solve physics problems about simple machines, mechanical advantage, efficiency
Vocabulary:
machine : multiplies force or makes work easier by changing the direction of force
compound machine : 2 or more combined simple machines
IMA: Ideal Mechanical Advantage is a ratio of input over output distances
AMA : Actual Mechanical Advantage is a ratio of output force over input force
 

SIMPLE MACHINES


Simple machines can be divided into 2 main categories, the lever types and the ramp types. A lever comes in 3 classes, determined by the arrangement of the Effort, Fulcrum and Resistance. A 1st Class lever has the Fulcrum in the middle, 2nd class has the Resistance in the middle and 3rd class has the Effort in the middle.The amount of work ( F x d ) that you put into a simple machine is always less than you get out (due to frictional losses). The advantage of a simple machine is that it can amplify forces or distances but not both. To amplify force, distance is sacrificed and to amplify distance, force is sacrificed. Inclined planes (ramps) reduce effort by increasing the effort distance.
Neglecting friction, the 6 types of simple machines follow this equation:

Win = Wout
Fe x de = Fr x dr

Now, including friction we can evaluate the efficiency (Eff) and mechanical advantage (MA) of a simple machine. Efficiency is just a ratio of the work the machine puts out to the work you put in. Ideally, the maximum efficiency would be 1 (100%), but is usually less because of frictional losses. In other words decreasing machine friction increases efficiency.

Eff = Wout / Win
or
Eff = Fr x dr / Fe x de

Mechanical advantage is a ratio which defines the factor by which the force has been amplified. Any factor less than 1 amplifies the output distance dr, greater than 1 amplifies the output force Fr.

IMA = de/dr
Ideal Mechanical Advantage assumes 100% efficiency (no loss to friction)
The IMA of a pulley equals the number of supporting rope segments


AMA = Fr/Fe
Actual Mechanical Advantage takes into account frictionl losses.
30 N applied to a crowbar raises a 300 N rock has an AMA of 10

Click Here for See-Saw Lever DEMO!
Put several masses on a see-saw in an effort to balance the system.
Click Here for Inclined Plane DEMO!
This lets you alter the initial velocity, mass, and angle of a frictionless inclined plane.


 
Practice: Help:
PB1 For a first class lever... If Fe= 59 N and de= 8.1 m and dr= 2.7 m, how many N can be lifted?


Fr=(Fede)/dr
PB2 What force is required at a .2 m radius wheel to lift 500 N if the axle radius is .015 m?


Fe=(Frdr)/de
PB3 A pulley with 3 support ropes, _ cm of rope must be pulled to raise a 57 kg mass 68 cm ?


support ropes
PB4 _ N is required to push a 33 kg mass up a ramp that is 8.7 m long and 7.1 m high ?



Fe=(m9.8dr)/de
PB5 A .05 m wide wedge must be _m long if 500 N of hammer force pushes 3000 N sideways


de=(Frdr)/Fe
PB6 100 N Fe on a screw jack turns the .03 m circumference cylinder 20 times raising 1000 N _m higher


dr=(Fede)/Fr
de=.03 x 20
PB7 What is the efficiency of a pulley if 3000 J of input causes 2800 J of output


Eff=Wout/Win
PB8 What is the efficiency of a screw jack if it takes .2 m of turning with 50 N of effort to raise a 500 N object .018 m?


Eff=Frdr/Fede
PB9 The IMA of a ramp if it is 8.4 m long and 4.9 m high is _


IMA=de/dr
PB10 The AMA of a crowbar that requires 50 N to raise 420 N is _


AMA=Fr/Fe
answer bank:
90
37.5
426
5519.36
263.9241
204
4950
177
43365
8.4
.3
41.29407
1.714286
19.02497
.06
93.3

Scientist Spotlight:
Galileo Galilei 1564-1642
Italian scientist and philosopher. Galileo was a true Renaissance man, excelling at many different endeavors, including lute playing and painting.

Resources (Study Links/Study Tips/Reading Lists)
Click Here for See-Saw Lever DEMO!

Click Here for Inclined Plane DEMO!

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