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. Systematic
B. Random
C. Both
D. 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 lazy
B. There is not enough time to collect enough
data
C. Statistics is too hard for this course
D. 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 cm
B. 98.9 ± 1.0 cm
C. 98.9 ± 1.1 cm
D. 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 collision
What might you be investigating in each of
these experiments?
Can all errors be classed as
independent or dependent?
A. Yes
B. 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.