Read the graph carefully

Let’s explore the intricacies of graphs today.

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Question

Andy created the setup as shown below to compare three types of springs, A, B and C.

He placed different masses on each spring and measured the length of the spring.

The results are shown in the graph below.

Using the same set-up, Andy wanted to find the small difference in mass between the two apples.

The apple on the left has a mass of 55g.

Which spring, A, B or C should Andy use?

1) A

2) B

3) C

What is the science concept tested here?

Elastic spring force

You learnt that the greater the spring extends, the spring exerts a greater elastic spring force on the object.

In order to choose the best spring, we need to ensure the spring must have a large extension when additional mass is added onto the spring.

Why is that so?

The explanation will be provided at a later part of this article.

First, let’s analyse spring A.

Is option A the best answer?

Let’s analyse the graph.

Based on the graph above, the spring extends when more mass is added onto the spring until 40g. Beyond that, the spring stops extending.

This shows the spring has reached its elastic limit of 40g. Beyond that, the spring might be permanently damaged and cannot increase its length anymore.

Now, looking back at the question, the mass of the apple is 55g.

When we hang the apple onto spring A, the spring will be permanently damaged.

The spring does not extend at all when a mass greater than 55g is added.

Moreover, the question states the apple has a small difference in mass.

Do you think it is possible for the other apple to have a mass of less than 40g?

Between the mass of 55g and 40g, that is a huge difference of 15g.

Based on this question, a small difference in mass should be around 1g to 2g difference.

Hence, even if the apple has a slightly smaller mass, the mass of the apple will still be more than 40g.

That is still beyond the elastic limit of spring A.

Conclusion:

We cannot use spring A.

Let’s compare Spring B and Spring C.

Now, to ensure that you can easily observe the small difference in mass, what must you do?

You want to make sure the changes in the extension of the spring is the largest!

Why?

When there is a small increase in mass, the extension in the spring will be significant. That way, you can see the difference easily.

This is illustrated in a separate example as shown below.

When we use identical springs in setups J and K, you can see a small increase in mass extends the spring by so little.

To a student, that is similar to this person:

It is so hard to accurately measure the increase of 0.1cm. A student could even measure a slight decrease in length!

However, if you use a spring that can be stretched easily (or less stiff), a small increase in the mass added onto the spring will result in a larger extension of the spring.

When you compare setup J and setup L, you can easily see the change in the extension of the spring.

A student might be like this:

You can tell straight away that there is an increase in the length of the spring when another object of slightly bigger mass is added.

By using a spring that is less firm, you can easily observe the change in the extension of the spring and determine correctly which object has a greater mass.

It’s time to apply what was explained to the question.

We have to choose the spring that extends the most given that both springs have the same increase in mass hung on it.

So, comparing Springs B and C, which spring extends the most?

To analyse the relationship in the graph, we have to give ourselves an example.

We imagine what happens when we increase the mass of the object hung on each spring.

This is represented by the increase in mass from 1 to 2.

When we observe spring B, you would have noticed the increase in length of spring B as shown in the green text box and the green arrow.

When we observe spring C, you would have noticed the increase in length of spring C as shown in the red text box and the red arrow.

What difference did you see?

When there is the same increase in mass of the objects hung onto each spring, spring C extends more than spring B.

Spring C allow us to easily see the tiny difference in mass of the object as Spring C extends more than spring B.

Conclusion

Hence, we can determine that spring C is the correct answer.

What if the apple has a slightly smaller mass than 55g?

Will this change the results?

Let’s use the same graph again. This time round, I decrease the mass from 3 to 4. Observe the red and green lines graph and see what happens.

Did you see that spring C shows a greater decrease in its length compared to spring B?

This means that when an apple with a mass slightly smaller than 55g is hung onto spring C, spring C will show a greater decrease in its length compared to spring B.

You can see the decrease in length easily when you use spring C compared to spring B.

Hence the answer is the same.

Learning pointers

• You have to learn how to interpret the line graphs. Always give yourself an example by changing one of the variables. Draw out the lines using a pencil to determine the relationship between the mass of the object and the final length of the spring.

• Take note of the conditions in the question. The question has clearly stated the mass of the apple is 55g. A small change in mass cannot possibly be 40g or less!

Adding a twist here:

Given that the springs used are the same as the question above.

If the question states the mass of an object is 20g and it wants you to identify which spring (A, B or C) is best used to find the tiny difference in the mass of this object, which spring should you use now?

Answer:

Spring A

The explanation behind this answer is the same. 🙂 

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