Chapter 12 – Simple Machines. A PowerPoint Presentation by Paul E. Tippens, Professor of Physics Southern Polytechnic State University. © 2007.
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
A PowerPoint Presentation by
Paul E. Tippens, Professor of Physics
Southern Polytechnic State University
SIMPLE MACHINES are used to perform a variety of tasks with considerable efficiency. In this example, a system of gears, pulleys, and levers function to produce accurate time measurements.
Photo Vol. 1 PhotoDisk/Getty
In a simple machine, input work is done by the application of a single force, and the machine does output work by means of a single force.
A simple machine
Wout= FoutsoutA Simple Machine
Conservation of energy demands that the work input be equal to the sum of the work output and the heat lost to friction.
A simple machine
The advantage is a reduced input force, but it is at the expense of distance. The input force must move a greater distance.
sin = 5.0m
Example 1.The efficiency of a simple machine is 80% and a 400-N weight is lifted a vertical height of 2 m. If an input force of 20 N is required, what distance must be covered by the input force?
The efficiency is 80% or e = 0.80, therefore
A simple machine
WEx. 2 (cont.)A12-hp winch motor lifts a 900 lb load
to a height of 8 ft. How much time is required if the winch is 95% efficient?
We just found that Po = 6270 W
Now we solve for t :
Time required: t = 1.15 s
The actual efficiency is always less than the ideal efficiency because friction always exits. The efficiency is still equal to the ratio MA/MI.
In our previous example, the ideal mechanical advantage was equal to 4. If the engine was only 50% efficient, the actual mechanical advantage would be 0.5(4) or 2. Then 160 N (instead of 80 N) would be needed to lift the 400-N weight.
Fo = 700 N; r2 = 20 cm
F = ?
r1 = 100 cm - 20 cm = 80 cm
Example 3.A 1-m metal lever is used to lift a 800-N rock. What force is required at the left end if the fulcrum is placed 20 cm from the rock?
1. Draw and label sketch:
2. List given info:
3. To find Fi we recall the definition of MI :
For lever:MA = MI
With no friction MI = MAand
For Wheel and Axel:
Wheel and AxelWheel and Axel:
For example, if R = 30 cm and r = 10 cm, an input force of only 100 N will lift a 300-N weight!
If the smaller radius is 1/3 of the larger radius, your output force is 3 times the input force.
MI = 4
To find Do we use the fact that
Example 4.A 200 Nm torque is applied to an input pulley12 cm in diameter. (a) What should be the diameter of the output pulley to give an ideal mechanical advantage of 4? (b) What is the belt tension?
Do = 4(12 cm) = 48 cm
Now, ti = Firi and ri = Di/2. Belt tension is Fi and ri is equal to ½Di = 0.06 m.
In this case, Dois the diameter of the driving gear and Diis diameter of the driven gear. N is the number of teeth.
If 200 teeth are in the input (driving) gear, and 100 teeth in the output (driven) gear, the mech-anical advantage is ½.Gears
Mechanical advantage of gears is similar to that for belt drive:
Ni = 40
Example 5.The driving gear on a bicycle has 40 teeth and the wheel gear has only 20 teeth. What is the mechanical advantage? If the driving gear makes 60 rev/min, what is the rotational speed of the rear wheel?
Remember that the angular speed ratio is opposite to the gear ratio.
Output angular speed:
wo = 120 rpm
wo = 2wi = 2(60 rpm)
Fo = 400 N
Example 6. An inclined plane has a slope of 8 m and a height of 2 m. What is the ideal mechan-ical advantage and what is the necessary input force needed to push a 400-N weight up the incline? The efficiency is 60 percent.
Fi = 167 N
Efficiency is the ratio of the power output to the power input.Summary for Simple Machines