If I hang twice as many stones on a rubber band, does it stretch twice as far?
Your guess
Pick one before you read on. It is fine to be wrong.
By the end you can
Measure how far a rubber band stretches as you hang more stones
Plot the results and describe the pattern
Kofi hangs a stone on a rubber band and it gets longer. He hangs a second stone and it gets longer again. He wants to know the pattern.
The original length is how long the band is with only the empty bag on it. The stretch is how much longer it gets.
To find the stretch, take the original length from the new length. The stones you hang are the load. A bigger load is a bigger pull.
Draw it first
Draw a band with more and more stones
1 Hang a band with an empty bag. Read its length on a ruler. This is the original length: 8 cm.
2 Put in one stone. The band gets longer, to 10 cm.
3 Do it with more stones. Each time the band gets longer. With 5 stones it is 16 cm.
Write the results in a table, one row for each number of stones. Then work out the stretch each time.
See it three ways
As a picture
In words
These are one learner's results. More stones give more stretch. The band does not grow by the same amount each time. Your band will give different numbers.
In symbols
stretch = new length − original length. With 3 stones: 13.4 − 8 = 5.4 cm.
A graph shows the pattern better than a table. Put the number of stones across and the stretch up. Plot a point for each row.
A spring gives a straight line. The rubber band bends away from the dashed straight line.A spring: 0 stones, 10 cm. 2 stones, 14 cm. 4 stones, 18 cm. Each stone adds the same 2 cm.
A steel spring stretches by equal amounts for equal loads. Here each stone adds 2 cm. This holds until the spring is stretched too far. A spring pulled too far stays long.
A rubber band is different. In these results the first stone adds 2 cm. The fifth adds only 1.2 cm. Your band may bend another way. The graph is not a straight line, so we say it bends.
Try it
Stretch a rubber band with stones
You need: a rubber band, a nail or a pencil to hang it from, held firm between two piles of books, a small bag with string, and 5 stones of the same size, a ruler, or a strip of card marked in centimetres, paper and a pencil.
Be safe: Keep your face away from the band. Stones can hurt feet, so work over a table or a soft cloth. Stop if the band looks thin.
Hang the band from the pencil. Hang the empty bag from the band.
Hold the ruler beside it with 0 at the top of the band. Read the length. This is the original length.
Put in one stone. Read the length again and write it down.
Add one stone at a time up to five. Read the length each time.
Work out the stretch for each row. Plot stones across and stretch up.
What you will see: The band gets longer with every stone, so the points climb. Join them with a smooth line. Look at it. Is it a straight line or does it bend? The dashed line is a straight line for comparison.
If you cannot try it, this is what happens.
A wrong idea many people have
Twice the load always makes twice the stretch.
Why it feels right: A spring does behave like this, so it is tempting to think every stretchy thing does.
The test that breaks it: Look at the band results. 2 stones stretch it 3.8 cm. Twice the stretch would be 7.6 cm. But 4 stones stretch it only 6.8 cm.
What is true: A spring stretches by equal amounts for equal loads. A rubber band does not quite. Its graph bends, so measure before you trust a pattern.
Key words
original length
how long a band or spring is with no stones, only the empty bag.
stretch
how much longer it gets: new length minus original length.
load
the weight hanging on a band or spring.
Back to your guess
The answer is B: It stretches more, but not always in an even way.
More stones give more stretch, but a rubber band does not stretch quite evenly. The best way to see the pattern is to measure and plot it.
Check yourself
Try each one before you look. A wrong answer tells you where to go next.
A band is 8 cm long with no stones. With 3 stones it is 13.4 cm long. What is the stretch?
See the answer
5.4 cm
Stretch = new length − original length = 13.4 − 8 = 5.4 cm.
If you chose A: That is the new length. The stretch is how much longer it got: take away the original length. Go to S3.7.5.
If you chose B: You added the two lengths. Take the original length away from the new length. Go to S3.7.5.
Look at the graph of the spring. How far does it stretch with 4 stones?
See the answer
8 cm
Go up from 4 stones to the line, then across. The stretch is 8 cm. Each stone adds 2 cm.
If you chose B: You read the number of stones across. Go up from 4 on the stones scale to the line, then read the stretch. Go to S3.7.5.
If you chose C: That is the stretch for 3 stones. Find 4 on the bottom scale. Go to S3.7.5.
A spring stretches 2 cm for each stone. How far will it stretch with 6 stones? Assume it is not overstretched.
See the answer
12 cm
A spring stretches by equal amounts for equal loads. 6 × 2 = 12 cm.
If you chose A: You added the stones and the stretch for each stone. A spring adds the same stretch for every stone, so multiply. Go to S3.7.5.
If you chose C: You divided. Each stone adds 2 cm, so 6 stones add 6 lots of 2 cm. That is a multiplication. Go to S3.7.5.
Look at the rubber band results in the table. Which sentence describes them best?
See the answer
More stones give more stretch, but each stone adds a little less.
The stretch grows from 0 to 8 cm, so more stones give more stretch. The steps are 2, 1.8, 1.6, 1.4, 1.2 cm. They get smaller, so each stone adds a little less.
If you chose A: That is true for a spring. In this table the extra stretch for each stone gets smaller. Look at the stretch column. Go to S3.7.5.
If you chose B: Read down the stretch column. It gets bigger, not smaller. Go to S2.5.2.
From an earlier chapter
Each stone has a mass of 0.1 kg. About what does one stone weigh on Earth?
See the answer
1 N
On Earth each kilogram weighs about 10 N. 0.1 × 10 = 1 N.
If you chose B: That is the mass in kilograms, not the weight. Each kilogram weighs about 10 N. Go to S3.7.4.
If you chose C: That would be a mass of 1 kg. Multiply 0.1 by 10. Go to S3.7.4.
You stretch a spring much too far and then take the load off. What happens?
See the answer
It stays longer than before.
A spring only stretches evenly and springs back if it is not overstretched. Too much load changes it for good.
If you chose A: That is true for a spring that is not overstretched. Too much load changes its shape for good. Go to S3.7.5.
If you chose C: A spring does not shrink below its first length. An overstretched one stays longer. Go to S3.7.5.
Keep it
Copy this into your exercise book.
Stretch is new length minus original length. A spring stretches by equal amounts for equal loads, so its graph is straight. A rubber band bends. Measure and plot to see the pattern.
Draw: Axes: stones across, stretch up. A straight line for a spring and a bending line for a band.
