# Drawing and Evaluating Conclusions

In this worksheet, students will learn about Hooke's law and the effect of a force on a spring. They will practise drawing conclusions and evaluating their results.

Key stage:  KS 4

Curriculum topic:  Working Scientifically: Analysis and Evaluation

Curriculum subtopic:  Collecting, Presenting and Analysing Data

Difficulty level:

### QUESTION 1 of 10

Want to be good at experimenting? Looking into values like Hooke's law is a brilliant way of practising your experimental skills as you need to be accurate and precise.

The diagram shows a spring being stretched by applying a force on it; this is the force of gravity showing the effect of different masses (with different weights) attached to the spring.

Hooke's Law suggests:

The extension of an elastic object is directly proportional to the force applied to it.

Springs are elastic objects because they stretch. The extension is the increased length of the spring after the force has been applied.

In the diagram above, when one mass is attached to the spring, the extension is x. When a second equal mass is added, the extension is 2x.

This is the table of results from the experiment and a graph for the extension of the two springs.

Here x is for Force in Newton (N) and y1 and y2 show the extension of spring 1 and 2 in millimetres (mm).

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Which spring has an overall longer extension?

spring 1

spring 2

Are there any exceptions to the general conclusion in the previous question?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

yes

no

For both springs, what is the general conclusion that can be drawn?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Spring 1 extends more than spring 2.

Spring 2 extends less than spring 1.

Both springs extend more as the force applied is increased.

Which of the two springs provides more accurate results?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

spring 1

spring 2

How can you tell that spring 2 has given more accurate results?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Each point of the extension of spring 1 is on the line of best fit.

Each point of the extension of spring 2 is on the line of best fit.

Spring 1 gives a straight line.

Suggest two reasons why spring 2 has produced more accurate results.

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

There could have been errors in measurements of spring 1.

Spring 2 has maintained its elastic position better than spring 1.

The results recorded were wrong.

The graph was not plotted correctly.

Spring 2 has gone into its plastic state.

Do some research on the internet and find out what elasticity of a material is.

The way an elastic material stretches when pulled.

The tendency of solid materials to return to their original shape after being deformed.

The reasons an elastic material stretches when pulled.

What does it mean that a material is in a plastic state?

The material is deformed due to applied forces and cannot return to its original shape.

The material is deformed due to applied forces and can return to its original shape.

The material breaks easily when pulled.

Do both springs in this experiment abide by Hooke's Law?

yes

no

What more evidence could you collect for this experiment?

Try a third elastic material.

Try a wider range of forces.

Compare elastic materials and ones in the plastic state.

Research for more similar experiments.

The conclusion is reliable enough, no additional evidence needed.

• Question 1

This is the table of results from the experiment and a graph for the extension of the two springs.

Here x is for Force in Newton (N) and y1 and y2 show the extension of spring 1 and 2 in millimetres (mm).

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Which spring has an overall longer extension?

spring 2
EDDIE SAYS
Spring 2 has a longer extension than spring 1. You can read this from the table of results or see it on the graph.
• Question 2

Are there any exceptions to the general conclusion in the previous question?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

yes
EDDIE SAYS
Yes, the first two readings actually show that spring 1 extends more than spring 2, but overall y2 is longer than y1.
• Question 3

For both springs, what is the general conclusion that can be drawn?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Both springs extend more as the force applied is increased.
EDDIE SAYS
By analysing the results table for both springs, it is evident that both springs extend more as a bigger force in applied to them.
• Question 4

Which of the two springs provides more accurate results?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

spring 2
EDDIE SAYS
Spring 2 provides more accurate results. You will learn why in the next question.
• Question 5

How can you tell that spring 2 has given more accurate results?

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

Each point of the extension of spring 2 is on the line of best fit.
EDDIE SAYS
It is clear on the graph that some points of y1 are not on the line of best fit, whereas for y2 all points fit on the line. When points are close to the line of best fit, they are more accurate.
• Question 6

Suggest two reasons why spring 2 has produced more accurate results.

 x Spring 1 (y1) Spring 2 (y2) 1 1.00 3.00 2.2583 2 2.00 4.50 4.3166 3 3.00 6.00 6.3749 4 4.00 7.50 8.4332 5 5.00 9.00 10.4915 6 6.00 10.50 12.5498 7 7.00 13.00 14.6081 8 8.00 14.00 16.6664 9 9.00 15.00 18.7247

There could have been errors in measurements of spring 1.
Spring 2 has maintained its elastic position better than spring 1.
EDDIE SAYS
Usually when results are not accurate, there have been experimental errors. Additionally, in this case the material is an important factor, as different materials have different elasticities.
• Question 7

Do some research on the internet and find out what elasticity of a material is.

The tendency of solid materials to return to their original shape after being deformed.
EDDIE SAYS
Elasticity is the tendency of solid materials to return to their original shape after being deformed. The more elastic a material the more force it will be able to store when it deforms.
• Question 8

What does it mean that a material is in a plastic state?

The material is deformed due to applied forces and cannot return to its original shape.
EDDIE SAYS
Plasticity is the state where a material is deformed due to applied forces and cannot return to its original shape.
• Question 9

Do both springs in this experiment abide by Hooke's Law?

yes
EDDIE SAYS
Both springs abide by Hooke's Law. You can tell both by the table of results (the measurements show that the bigger the force, the longer the extension) and the graph (both lines show a positive correlation of extension and force).
• Question 10

What more evidence could you collect for this experiment?

Try a third elastic material.
Compare elastic materials and ones in the plastic state.
Research for more similar experiments.
EDDIE SAYS
It would be good to try a third elastic material and one in the plastic state, in order to draw a stronger conclusion based on more evidence. Additionally, more secondary evidence would provide another set of data to compare your own with, as long as the experiments are similar.
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