Uncertainties

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.