4PH1
Forces, Movement & Changing Shape
Forces & Motion · 1 question type
Exam Frequency Analysis
Past paper frequency (2018 to 2024)
This topic accounts for approximately 14% of your exam marks.
stable
High
Stable14%
F = ma, resultant forces and Hooke's Law calculations are high-frequency multi-mark questions.
Aim
- Measure the of a spring (or a rubber band, or a length of metal wire) as the stretching on it is increased, and decide whether the two are directly proportional
Variables
- Independent variable: stretching force, F (N), set by hanging known masses
- Dependent variable: extension, e (cm or mm), read off a fixed ruler
- Control variables: the same spring (or rubber band, or wire) used throughout; the same starting attachment point; the same ruler with the same zero alignment
Apparatus
| Equipment | Purpose | Resolution |
|---|---|---|
| Retort stand, clamp and boss, G-clamp | Holds the spring vertically and prevents the stand from toppling as masses are added | — |
| Spring (or rubber band, or thin metal wire) | The object whose extension is being measured | — |
| 100 g slotted masses with a 100 g hanger | Provides the known stretching forces in 1 N steps (since W = 0.1 × 10 = 1 N per mass) | — |
| Vertical ruler clamped beside the spring | Measures the position of a pointer attached to the bottom of the spring | 1 mm |
| Small horizontal pointer (or piece of tape acting as a fiducial marker) | Lets you read the bottom of the spring against the ruler accurately | — |
| For a metal wire: a bench pulley and a wooden block clamped over the wire | Allows the wire to be stretched horizontally with the masses hanging vertically off the bench edge | — |
Method
- Hang the spring (or rubber band, or metal wire) from the clamp without any mass attached. Read and record its original length L₀ using the pointer and the clamped ruler
- Place the 100 g mass hanger on the spring. Give the spring a couple of seconds to come to rest, then read the new pointer position L₁ and record it together with the mass
- Add one further 100 g mass to the hanger. Allow it to come to rest, then read and record the new length
- Continue adding masses in 100 g steps until all five are loaded
- Carefully remove the masses one at a time and check that the spring returns to its original length. If it does not, it has been stretched beyond its and the run must be repeated with a fresh spring
- Repeat the whole sequence three times and take the mean of the three readings at each load
- For the metal wire variant: clamp the wire horizontally across the bench, run it over a bench pulley, attach the hanger to the dangling end, and stick a small piece of tape on the wire as a fiducial marker for the ruler
Analysis
- Convert each loaded mass m (in kg) to a stretching force F with F = m × g, taking g = 10 N/kg (so each 100 g step adds 1.0 N)
- Calculate the extension e at every load:
e = mean loaded length − original length
- Plot force (y-axis) against extension (x-axis), or extension against force, but force-vs-extension is the conventional Hooke's law plot
- A straight line through the origin shows that force and extension are directly proportional, i.e. the material is obeying Hooke's law throughout the tested range
- A region where the line curves away from a straight line shows the material has passed its limit of proportionality (see section 9)
Sources of error and safety
- Systematic error, parallax. Always read the pointer against the ruler with your eye exactly level with the pointer
- Random error, equipment movement. A wobble of the stand between readings shifts the apparent zero; the G-clamp removes this
- Random error, slow settling. Let the spring fully stop oscillating before taking each reading; a length read mid-bounce will be off by the amplitude of the wobble
- Safety: wear safety goggles in case the spring or wire snaps and whips back, keep feet clear of the hanging masses, and place a soft mat or tray beneath the masses to catch them if they drop