The Purpose of this Minilab

1
The Purpose of this Minilab

• Gain experience in calculating and propagating
  errors associated with measurements.
• Gain experience in performing rough estimations.

2
Finding Uncertainties from Repeated Measurements

• Repeated measurements can give you different
  results due to
• Object variation (e.g., the width of a table may
  be different at
• different positions, or it may vary with
  temperature or moisture
• in the air).
• Measurement device or procedure may create
  scatter in the
• result.

? Take many (5 or more) measurements and
calculate the mean
3
Mean
Standard Deviation
A measure of how far individual data scatter.
Standard Deviation of the Mean
This is the uncertainty/error in the mean value.
Result
4
Error Propagation
A general physics formula..
And some measurement with uncertainties..
Plug in x, y, z.. to get value of f
Calculate uncertainty in f
Result
5
Estimationsan example

• How many (NT) new car tires are bought in Utah
  every year?

P Population 2 Million A that are adults and
drive a car 60 M Number of miles driven per
adult per year 15000 miles N Number of tires
per car 4 L Number of miles during life of
tire 45000 miles
6
What we will look at closely when grading

• Did you make reasonable estimations/calculations
  of uncertainties?
• Did you report significant figures correctly?
• Did you propagate your errors without mistakes?
• When you performed an estimation, did you perform
  logical
• reasoning to arrive at your estimate.