Measuring Forces, Spring Scales
You'll be able to use a spring scale correctly: zero, hang, read at eye level.
In 1660, Robert Hooke stretched hundreds of springs and noticed that doubling the stretch always doubled the pull-back force, a pattern now built into every spring scale on Earth.
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Q1 · Hold a book in your hand with your arm straight. As you add more books, what happens to the force on your arm? How could you measure that force?
Q2 · Two scales: one shows kilograms, one shows Newtons. What different things are they measuring?
● Know
- The Newton (N) is the SI unit of force
- A spring scale (Newton meter) measures force in Newtons
- Hooke's Law qualitatively: spring extension is proportional to applied force
● Understand
- How a spring scale works (extension → force reading)
- Why a spring scale would read differently on the Moon (but a balance would not)
- What calibration means and why it matters
● Can do
- Use a spring scale correctly: zero, hang, read at eye level
- Identify and avoid parallax error
- Distinguish between measuring force (N) and measuring mass (kg)
A spring scale measures in . When you hang an object from the hook, the spring and the pointer moves to show the .
Every spring has a personality. Stretch it a little, it pulls back a little. Stretch it a lot, it pulls back a lot. Robert Hooke noticed this in 1660, and now every spring scale in every science lab owes him a debt.
Hooke's Law, in the form Year 7 needs it, says that the extension of a spring is proportional to the force applied to it within its proportional range. Proportional is a precise word and it is the whole point of the law. It does not merely mean that more force gives more stretch, which would be true of almost anything springy. It means the stretch keeps step with the force exactly: apply 1 N to a particular spring and it might extend 1 cm, then 2 N extends it 2 cm, and 4 N extends it 4 cm. Doubling the force doubles the stretch, every time, with no drifting.
That exactness is what makes a spring scale possible, and it is worth seeing why. Because the relationship keeps step, equal steps in force produce equal steps in stretch, which means the markings on the scale can be spaced evenly. Look at any Newton meter in the lab and you will see that the gap from 0 to 1 N is the same as the gap from 8 to 9 N. If a spring stretched in some uneven way, the numbers would have to bunch up at one end and the instrument would be far harder to read and to make.
The instrument itself is then simple. You hang an object from the hook, and gravity pulling on that object stretches the spring downward. A larger weight stretches it further, a pointer fixed to the moving end travels down the evenly spaced scale, and you read the force straight off in newtons without calculating anything. What you are reading is the force the object's weight exerts on the spring.
The straight-line relationship ends at the limit of proportionality. Beyond that point, extension no longer increases in the same ratio as force. This is different from the elastic limit: a spring can behave nonlinearly yet still return to its original length when the load is removed. Beyond the elastic limit, some deformation remains after unloading. So a departure from a straight-line graph alone does not prove permanent damage. Evenly spaced spring-scale markings rely on the proportional range and correct calibration. Stay within the manufacturer's stated force rating: overloading can damage the spring or make readings unreliable, even when damage is not obvious.
Text description
- The scale is supported at the top. A load hangs from a rod connected to the lower end of the spring. The pointer is fixed to that same lower end, aligned with the 4 N mark.
- The scale has equally spaced marks at 0, 2, 4, 6 and 8 N. Read the settled pointer straight on, at eye level.
- The graph has force in newtons on the horizontal axis and extension in centimetres on the vertical axis. Points (0,0), (1,1), (2,2), (3,3) and (4,4) all lie on one straight line through the origin.
- Within the proportional range, doubling the force doubles the extension. This graph is illustrative, not a calibration for every spring scale.
Using a spring scale seems simple, but there are five important steps that prevent measurement errors:
- Zero the scale. Before attaching anything, check that the pointer reads exactly 0 N. If not, adjust using the zeroing screw. This is essential, a scale not zeroed will give readings that are too high or too low by a fixed amount.
- Hang the object vertically. Hold the spring scale upright and attach the object at the hook. If the scale is tilted, gravity doesn't act fully along the spring axis and you get a wrong reading.
- Wait for the scale to settle. Let it stop swinging before reading. A moving pointer gives an unreliable reading.
- Read from eye level (avoid parallax error). Position your eye directly in front of the pointer, at the same height as the pointer. Looking from above makes the reading appear lower; looking from below makes it appear higher.
- Don't exceed the maximum force. Every spring scale has a maximum force rating (e.g. 10 N). Exceeding the stated rating can damage the spring or make readings unreliable. Stay within the rating.
Spring scale vs balance scale:
- Spring scale: Measures the gravitational force (weight) in Newtons. On the Moon, where gravity is weaker, it would give a lower reading, the weight is less.
- Balance scale: Compares the object's mass against known masses. Mass doesn't change with gravity, so a balance gives the same reading on the Moon as on Earth.
Calibration means making sure an instrument reads correctly. For a spring scale:
- Hang a known mass (e.g. 100 g, which has a weight of about 1 N on Earth).
- Mark the pointer position as "1 N".
- Repeat with 200 g (2 N), 300 g (3 N), and so on.
- Connect the marks, this is the calibrated scale.
If the spring is old or damaged, the calibration may be wrong, this is why you always zero the scale first.
Parallax error in detail: The pointer sits slightly in front of the scale markings. If you look from above, the pointer appears to be opposite a higher number. If you look from below, it appears lower. The fix: align your eye with the pointer at exactly the same height, looking straight across.
Australian applications of force measurement:
- Fishing scales: Anglers use spring scales (in N or kg equivalent) to weigh their catch after fishing on the Great Barrier Reef or in Australian rivers.
- Luggage scales at airports: Sydney, Melbourne and Brisbane Airport staff use scales that measure in kg, but they measure the force of gravity on the bag and convert.
- Sports science: AFL and NRL teams use force plates and sensors (measuring in Newtons) to assess kick force, jump height and impact in training.
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1Fix the units before doing anything else250 g = 0.250 kg.The field strength is given in newtons per kilogram, so the mass has to be in kilograms before it can be multiplied by it. Leaving it in grams would give 250 × 9.8 = 2450, a number a thousand times too big, and the mistake would be invisible because 2450 is a perfectly ordinary-looking number. Converting first is not tidiness, it is the step that makes the rest of the working mean anything.
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2Write the relationship you are usingA spring scale reads a force, and the force here is the weight: W = m × g.Say what the instrument measures before you calculate, because that is what decides which equation applies. A balance would have been a different question entirely, and its answer would still be 250 g on the Moon. The scale is reading the pull of gravity on this mass, so weight is the quantity to find.
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3Substitute and calculate the expected readingW = 0.250 × 9.8 = 2.45, so the scale should read about 2.5 N.Check it against something you already know before moving on. A 100 g apple weighs roughly 1 N, and this mass is two and a half apples, so an answer near 2.5 N is exactly the right size. A predicted answer you have sanity-checked is what turns the next step into evidence rather than a guess.
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4Compare the prediction with the measurement, and by how much3.1 − 2.5 = 0.6, so the scale is reading 0.6 N too high.Work out the size and the direction of the difference rather than just noticing that it is wrong, because those two facts are what identify the cause. Too high by a fixed amount is a very different fingerprint from too high by a fixed percentage, and only one of the errors in the previous card produces each.
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5Match the fingerprint to a cause, and say how to test itThe scale was almost certainly not zeroed: the pointer already sat at about 0.6 N with nothing attached.An unzeroed scale adds the same fixed amount to every reading, which fits an error of exactly 0.6 N. Parallax would not fit, because looking from an angle gives a different error each time you move your head rather than a steady one. A damaged spring can affect the zero reading or the calibration, so a constant offset alone does not rule out damage. The test takes two seconds: take the mass off and look at where the pointer sits. If it reads 0.6 N with nothing on the hook, a zero offset is confirmed. Re-zero it and check known forces within its rating; subtracting a constant offset is justified only if calibration checks show the remaining readings are reliable.
Wrong: "A spring scale measures mass in kilograms." No, a spring scale measures force (weight) in Newtons. A balance scale measures mass in kilograms by comparing with known masses.
Right: Spring scale → Newtons (force). Balance scale → kilograms (mass). Different instruments measuring different quantities.
Wrong: "You can zero the scale after you attach the object." Zeroing must happen BEFORE attaching the object, zeroing after would just set the zero to include the object's weight, and all readings would be wrong.
Right: Zero the scale first (nothing attached), then attach the object and read the force.
Wrong: "Hooke's Law means springs always behave the same no matter how far you stretch them." Hooke's Law describes the proportional range. A spring can stop obeying that linear relationship while still returning to its original length when unloaded.
Right: Hooke's Law applies up to the limit of proportionality. The elastic limit is a different boundary: beyond it, deformation remains after the load is removed.
A spring scale reads 9.8 N when a 1 kg mass hangs from it on Earth. Predict what the scale will read when the same mass is hung from it on the Moon (g = 1.6 N/kg). Will a balance scale measuring the same object on the Moon give a different reading?
How close was your prediction?
Q1. Describe how you would use a spring scale to measure the weight of your science textbook. Include at least 3 specific steps and one source of error to watch for. (3 marks)
Q2. A student measures the weight of a 5 kg dumbbell on Earth (spring scale reads 49 N) and then on the Moon. (a) Would the spring scale reading change on the Moon? (b) Would a balance scale reading change on the Moon? Explain both. (3 marks)
Q3. A student applies the following forces to a spring and records the extension: 2 N → 1 cm; 4 N → 2 cm; 6 N → 3 cm; 8 N → 4 cm; 10 N → 5 cm; 12 N → 5 cm. (a) Describe the pattern for the first 5 readings. (b) How does the 12 N reading compare with the proportional pattern? (c) Do these readings prove permanent deformation? Explain how you would check. (4 marks)
Answers
▾MCQ 1
C A spring scale measures force in Newtons. It works because spring extension is proportional to force (Hooke's Law). A balance scale measures mass in kilograms.
MCQ 2
C Hooke's Law: extension is proportional to force within the proportional range. Double the force → double the extension within that range. This supports evenly spaced spring-scale markings. The elastic limit instead concerns whether deformation remains after unloading.
MCQ 3
B Parallax error happens because the pointer is in front of the scale markings. Read from directly in front with your eye at the same level as the pointer, this eliminates the angle.
MCQ 4
C The Moon's gravity is about 1/6 of Earth's. On Earth a 10 kg object weighs 98 N (≈ 100 N); on the Moon it weighs about 16 N. The spring scale measures force (weight), which depends on gravity.
MCQ 5
B Zeroing means setting the pointer to 0 N with nothing attached. This ensures subsequent readings reflect only the force from the object being measured, not any pre-existing offset.
Short Answer 1
Model answer: Step 1: Zero the spring scale before use, check the pointer reads 0 N with nothing attached (1 mark). Step 2: Hang the textbook from the hook and hold the scale vertically (1 mark). Step 3: Wait for the scale to stop moving, then read the force in Newtons from eye level to avoid parallax error (1 mark). Parallax error is the key source of error to watch for.
Short Answer 2
Model answer: (a) Yes, the spring scale reading would be lower on the Moon (1 mark). The spring scale measures weight (gravitational force), which is smaller on the Moon because the Moon's gravity is weaker (1 mark). (b) No, the balance scale reading would NOT change on the Moon (1 mark). A balance compares the object's mass against known masses, mass doesn't change with gravity, so both sides of the balance would be equally affected and the reading stays the same.
Short Answer 3
Model answer: (a) For the first 5 readings, each increase of 2 N gives an extra 1 cm of extension: the extension is proportional to force (1 mark). (b) Continuing that pattern predicts 6 cm at 12 N, but the recorded extension is 5 cm, so that reading departs from the proportional pattern (1 mark). (c) This alone does not prove permanent deformation or locate the elastic limit (1 mark). Remove the load and compare the spring's length with its original unloaded length; also check the apparatus and repeat the readings before drawing a conclusion (1 mark).
The hook at the start of this lesson revealed something interesting: take a spring scale to the Moon and it gives a different reading, but a balance scale gives exactly the same reading. Now you understand why!
Explain why the spring scale changes on the Moon but the balance doesn't, it comes down to what each instrument is actually measuring. Use the words mass, force, Newton and gravity at least once each.
- A spring scale measures force in newtons by how far a spring stretches; a balance measures mass in kilograms by comparing against known masses. They are different instruments measuring different quantities.
- Hooke's Law describes extension proportional to force within the proportional range, which supports evenly spaced scale markings. Beyond the elastic limit, deformation remains after unloading; a damaged scale must be checked before its readings can be trusted.
- Zero before you attach anything, hang the scale vertically, let it settle, and read with your eye level with the pointer to avoid parallax error. Each step removes one specific way the reading can be wrong.