# Draw and Evaluate Conclusions

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

Key stage:  KS 3

Curriculum topic:   Working Scientifically

Curriculum subtopic:   Analysis and Evaluation

Difficulty level:

### QUESTION 1 of 10

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

The diagram below shows a spring being stretched as a force is applied; it's the force of gravity showing the impact of different masses (with different weights) attached to the spring.

Hooke's Law suggests that 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.

Now it's over to you. Remember you can always turn back to the introduction if you need to re-read this information.

Below 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 spring 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 extension for spring 1 is on the line of best fit

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

Spring 1 gives a straight line when plotted on a graph

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 the 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 refers to.

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 other 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 is needed

• Question 1

Below 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 spring 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 spot this on the graph. Strong start! Let's push on.
• 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. However, overall y2 is longer than y1. There's a lot of information to take it in these questions so remember to take your time and read each question thoroughly.
• 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
Through analysing the results table for both springs, it becomes evident that both springs extend more, as a bigger force in applied to them. Take a deep breath, you’ve got this.
• 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'll learn why in the following 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 extension for spring 2 is on the line of best fit
EDDIE SAYS
It's 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, this means that they're more accurate. Don’t panic if you found this difficult, with each question you attempt you'll gain confidence.
• 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 the 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 experiment the material used 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 refers to.

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 material is, 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 the material is deformed due to applied forces and cannot return to its original shape. Why not try making revision cards with key terms such as these?
• 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 gather this from the table of results as the measurements show that the greater the force, the longer the extension. Additionally, the graph demonstrates a positive correlation between extension and force.
• Question 10

What other 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 great to try a third elastic material and one in the plastic state, in order to draw a stronger conclusion based on more evidence. Additionally, secondary evidence would provide another set of data to compare wit your own, as long as the experiments are similar. Great work, you've completed another activity! How about attempting another one so you feel super confident?
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