Uncertainties
Problem Solving class 1 for Physics 1A and Higher Physics 1A
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.
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?
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.
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 technique• Calibration errors• Zero errors
Standing wave in column with end effects
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?
A. SystematicB. RandomC. BothD. Neither
How do you account for Systematic Uncertainties?
From now on we are considering Random uncertainties
Calculating the error in a measurement
In the first year physics lab we use:
More correct to use standard deviation.
Why don’t we use the standard deviation in the first year physics lab?
A. We are lazyB. There is not enough time to collect enough
dataC. Statistics is too hard for this courseD. We should and I am going to use it in all the
experiments
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 cmB. 98.9 ± 1.0 cmC. 98.9 ± 1.1 cmD. 98.9 ± 1.05 cm
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.
Independent Errors
These come from different sources. If two different pieces of equipment are used then the errors are independent.
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
string• Acceleration of a cart and the mass of the cart• Period for a collision and the maximum
acceleration during a collisionWhat might you be investigating in each of these
experiments?
Can all errors be classed as independent or dependent?
A. YesB. No
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:
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
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 quadrature
Turn to part 3 of Introductory Experimentation in your Lab Manual
Work together to practice using uncertainties.