What are problem solving classes These form a bridge between lecture material labs and the exam In some problem solving classes you will be introduced to material covered in the lab part of the course ID: 661729
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Uncertainties
Problem Solving class 1 for Physics 1A and Higher Physics 1ASlide2
What are problem solving classes?
These form a bridge between lecture material, labs and the exam.
In some problem solving classes you will be introduced to material covered in the lab part of the course.
In all of them you will be practicing using the physics you have been shown in lectures to answer problems. This is a vital skill as this is what you will need to do in the exam.Slide3
Why are uncertainties important?
How long does it take the ball to reach the floor?
Are you certain?
If I dropped it from the same height would I get the same answer again?Slide4
Random uncertainties
We will usually be dealing with these in the lab.
Random uncertainties are as likely to be above the “correct” value as below them.
Another way to say this: Random uncertainties have a zero mean.For example: measuring your height with a ruler; the mass of the 50g masses in the lab.Slide5
Systematic Uncertainties
Used in the standing waves on a string experiment.
These uncertainties have a non-zero mean, they cause you to consistently measure an uncertainty that is too large or too small.
Can be caused by:Poor techniqueCalibration errorsZero errors
Standing wave in column with end effectsSlide6
Systematic or Random?
Is the error in the measurement
of the time it takes the ball to
fall using a stopwatch a systematic or a random error?SystematicRandomBothNeitherSlide7
How do you account for Systematic Uncertainties?Slide8
From now on we are considering Random uncertaintiesSlide9
Calculating the error in a measurement
In the first year physics lab we use:
More correct to use standard deviation. Slide10
Why don’t we use the standard deviation in the first year physics lab?
We are lazy
There is not enough time to collect enough data
Statistics is too hard for this courseWe should and I am going to use it in all the experimentsSlide11
Practice
Five people measure the height of a laboratory bench, they record it as 98.2, 99.1, 98.4, 100.3 and 98.5 cm high. What is the height of the bench with an uncertainty?
A. 98.9 ± 2.1 cm
B. 98.9 ± 1.0 cmC. 98.9 ± 1.1 cmD. 98.9 ± 1.05 cmSlide12
Dependent Errors
These come from the same source, for example if you use the same piece of equipment to make a measurement then the errors are dependant. Slide13
Independent Errors
These come from different sources. If two different pieces of equipment are used then the errors are independent.Slide14
Classify as independent or dependent
Height a ball bounces and the mass of the ball
Height a ball bounces and initial height of ball
The period of a pendulum and the length of a stringAcceleration of a cart and the mass of the cartPeriod for a collision and the maximum acceleration during a collisionWhat might you be investigating in each of these experiments?Slide15
Can all errors be classed as independent or dependent?
Yes
NoSlide16
Absolute and percentage uncertainties
These are two ways to present the uncertainty. In the first year physics lab you should present your final uncertainty as an absolute uncertainty.
Absolute uncertainty
, is the uncertainty in the value presented with the same units as the value:Percentage uncertainty is the percentage of the final value that the uncertainty has:Slide17
Calculating dependent uncertainties
If you add or subtract the values then you add the uncertainties
If you multiply or divide the values then you add the percentage errors to get the final percentage error Slide18
Calculating Independent Uncertainties
If you add or subtract the value then you add absolute errors in
quadrature
(use Pythagoras)If you multiply or divide the value then you add the percentage errors in quadratureSlide19
Turn to part 3 of Introductory Experimentation in your Lab Manual
Work together to practice
using uncertainties.Slide20