Statics

Intro (or Review) of Statics

Statics: 

The study of equilibrium, stationary systems subject to applied forces. 

Applications - design of buildings

Design of bridges

Design of load bearing structures that are supposed to remain static and stationary.

Force: Push or Pull

• Body Force - distributed internally throughout a structure
• Surface Force or Concentrated Force - force localized at a specific point.
• concurrent Force -  system of forces that can be represented by a single force
• non-concurrent - force systems with parallel components that cannot be simplified into a single force.
• Resultant Force - equivalent force of the total system - or vector sum of all the individual forces.   
  

Forces are represented by vectors (an arrow) with a defined orientation and direction - vectors can be 2D or 3D.

 Example in book: 18.1 pg 472
Find the resultant force

Rx = -100cos30° + 200cos45°+50 = 104.8
Ry = 100sin30°+200sin45°=191.4

R = SQRT(104.8^2 + 191.42^2) = 218.2

Just use your trig!

In 3D

 Rx = 200cos54.7° + 0 = 115.5
Ry = 200cos54.7° + 100cos45° = 186.3
Rz = 200cos54.7° + 100cos45° = 186.3

 

Moment:
rotation around an axis
M = Fd

d = perpendicular distance from the line of action to the force

See example 18.2 in book

Equilibrium
Summation of all the forces and moments is zero


Free Body Diagram

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Statics lab: Find Static Frictional Coefficients - μs

Myth buster questions to investigate in lab:


#1: Is the max incline before slip really independent of mass? 

A great big truck - vs a little lightweight car - if they both have the same tires, they will both slide around the same?


Many people add sandbags to their car / truck in the winter to try and increase their traction - do sandbags help (if they have 4WD)?  Do they help on a flat road?  Do they help on a hill?

Myth buster question #2:  Is the angle of slip really independent of surface area????

Bald tire vs. new tire - How dangerous is it to drive around with bald tires?  Is it really that important to keep getting new tires all the time?


 Road bike with skinny tires, vs. trail bike with fat tires - Why are there different bike (and car) tire designs based on what types of roads and trails you are on?  (Snow tires vs. regular tires) Compare tire performance on various surfaces - slick surface vs. rough surface. 


Other lab data -
Which shoes are safest for Granny to wear? 
Which gloves are the most slip resistant?



Taking Data in lab:

• Repeat each measurement 4 times
• Compare the data you get to the data other teams get - is it repeatable?  
• What is the error in measurement? 

Uncertainty Analysis:  
Errors in Physical Measurements

• X = True Value
• x_i = measured value
• n = number of measurements taken
• Accuracy = how close x_i is to true value X
• Precision = how good grouping is

Good accuracy poor precision -                                       Bad accuracy, good precision

 Mean:

 

• Median = midpoint in events (½points below, ½ points above)
• Mode = most frequently occurring value

• Error = e_i = Deviation from true value: e_i = x_i - X
  • We do not (and cannot) know X - so - Approximate X by the mean µ
  • e_i* = x_i - µ
  • e_i* approximates e_i and is called an estimator of e_i.
  • Random deviations: Human errors, normal distribution
  • Systematic deviations: Calibration errors

• Relative Error = DX/X -or- = e_i/m
• Variance

• Standard Deviation = width of distribution, estimate of average error

• Standard Deviation of Mean (SDOM)

Gaussian (Normal) Distribution, or common probability distribution.  
(Take a bunch of data, probability that data will fall within a certain range)

Example of different distributions taken with different precision -


 

• low standard deviation = data points very close to the mean
•  high standard deviation = data points spread out over a large range of values.

Week #1 HW:
Set up an excel worksheet to take data in lab.
Create tables to record results.
Enter equations that calculate the friction coefficient from angles.
Enter equations to calculate the average and standard deviations of your lab results.
Collect background information, and research car and bike tire designs.
Make a hypothesis about what you will find in lab next week.

If you are not familiar with excel, watch some youtube tutorials on whatever version you have of it!