Lesson 2: Error Calculations

 

Equation: T = 2π (extension/k)   ∴ k = 4π2 extension/T

 

 

1.     1.   For a 300g mass on a spring, estimate the extension and time period of oscillation to work out its spring constant (k)

 

esEstimate:
extension = 0.05 m.
T = 1 s.
m = 300 g

 

∴ k = 4π2 extension/T2
∴ k = 4π2 * 0.05 / (1)2

∴ k = 2 Nm-1 (1 s.f.)

 

2.       Now make some measurements, with uncertainties of T and m
Measurement:
extension = 0.03 m. ± 0.01 m.
T = 0.43 s. ± 0.10 s.
m = 300 g.

 

What is your calculated value of k?

∴ k = 4π2 extension/T2
∴ k = 4π2 * 0.03 / (0.43)2
∴ k = 2.75 Nm-1

 

Lesson 1: Measurements.

Topic 1: Physical Measurement

All the resources for this topic: Click Here

Lesson 1: Making Measurements

In Physics we are concerned with observing the world around us so we can develop theories and test those ideas to deepen our understanding of the universe and how it works.

First step is to become better observers. Good observers can make good estimates based on physical intuition. This is difficult to teach, but gets better with practice. The best observations are ones that can be measured, thus allowing us to quantify our theories and make precise predictions which can be accurately tested.

WORDS, words, words. It’s important to get them right:

Accuracy and Precision and What do examiners mean

Once you have read these documents, write answers to the following questions:

1. What is the difference between a precise measurement, and an accurate measurement?

2. How does this diagram illustrate precision and accuracy?

 

 The first diagram is precise but not accurate. Its precise because the dots are all close together. The second diagram is neither accurate or precise.

1) Precise means a consistent string of values that may or may not be accurate. Precision also means the value has a high significant figure or more  decimal places. Accuracy is how close a value is to the actual value.

 

2) The first diagram represents precision without accuracy as the dots are consistent and close together. It is not accurate because it is not close to the center of the diagram.

Th second diagram does not represent anything because the dots are randomly spread out.