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Class 5 Statics, Levers, andBalance
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2/15/2007 Class 5 2
Statics
The study of rigid bodies that are inequilibrium
Equilibrium = a state of rest or balance dueto the equal action of opposing forces dictionary.com
Why study things that dont move in a classabout how things move?
A static problem is a snapshot of a dynamic one Most of the time we can isolate a statics problem
that represents the worst case scenario in adynamic system
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2/15/2007 Class 5 3
Force as a vector
Whats a vector? Scalar: speed, mass, length, time
Vector: velocity, weight
When describing a force, think of Point of application (simplify)
Magnitude
Direction
Gravity is a force F=ma
Difference between mass and weight Quick Trigonometry lesson
SOHCAHTOA
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Free Body Diagram
A FBD is a simplified graphical depiction of all the
forces and moments happening on a body Applied, normal, friction, weight, gravity, spring, etc.
Examples: Book on a table (Newtons 3rd law)
Hanging from two ropes
Weight on a high crane
3 steps1. Isolate the body from all supports
2. Identify all external forces acting on the body
3. Sketch the body, showing all forces
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2/15/2007 Class 5 5
Torque, Moment
We already learned that Torque(moment)=Force*distance
Distance (d) stands for the PERPENDICULAR
distance between the force line of actionand the point of rotation, sometimes calledthe lever arm or moment arm
For something to be in Static Equilibrium,the sum of forces in any direction and thesum of moments about any point must = 0
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Solving a staticsproblem
Draw a FBD Choose a reference frame (x
horizontal, y vertical)
Choose a convenient point to calculatemoments around
Sum forces and moments in alldirections until unknowns are found
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2/15/2007 Class 5 7
Levers
Last week we learned about how gear ratiosgive you a mechanical advantage
Mechanical advantage, or the difference
between the work you get out and the workyou put in, can also be achieved with levers
A lever is a rigid object used with a pivot
point or fulcrum to multiply the mechanicalforce on an object
Three classes of levers
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2/15/2007 Class 5 8
1st Class Levers
Pivot is betweeninput and outputforces
Ex: seesaw,crowbar,shoehorn, oars,
can opener Double lever:pliers, scissors
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2/15/2007 Class 5 9
2nd Class Levers
The output islocated betweenthe input and
the fulcrum Ex:
wheelbarrow,
stapler
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3rd Class Lever
The input force ishigher than theoutput force
Input force moves
over shorterdistance thanoutput load
Ex: humanmandible, bicep,tweezers
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2/15/2007 Class 5 11
Ex: Biomechanics
Sum the momentsabout the elbowjoint
link
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Anecdotal evidence is the enemyof good design
- modified JP quote
Assignment:Find something in real life that experiences forces when used in
context (i.e. wine bottle opener, your toothbrush, a hanging streetlight, etc.) and draw its FBD. Try to guess/measure numbers thatmake sense to solve for an unknown force or moment in yoursystem (using your thumb as the lever point, how hard does thebrush press against your teeth? What is the moment at the base
of the street light post?). Post your sketch on your student pagefor discussion in class. Note: I realize this is a first and dontexpect perfect answers. The object is to get you thinking aboutthe things around you in terms of forces, moments, angles, etc.and be able to simplify them so you can learn how to apply thispractical skill to your art.