A student investigates a spring of width w made from a metal wire, as shown in Fig. 1.1. [Figure 1.1] The student constructs several springs, each made from a metal wire of different cross-sectional area A. The student investigates how the extension x of each spring varies with A when a load of mass m is applied. It is suggested that the relationship between x and A is x = mgw³NAn / γρ where g is the acceleration of free fall, ρ is the density of the metal, N is the number of turns of wire in the spring and γ and n are constants. Design a laboratory experiment to test the relationship between x and A. Explain how your results could be used to determine values for γ and n. You should draw a diagram, on page 3, showing the arrangement of your equipment. In your account you should pay particular attention to: • the procedure to be followed • the measurements to be taken • the control of variables • the analysis of the data • any safety precautions to be taken.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.

1. A is the independent variable and x is the dependent variable or vary A and measure x
2. keep m constant
3. labelled diagram of workable experiment including: spring fixed at one end (to a support) load attached to the other end labelled load/mass
4. clamped labelled ruler perpendicular by eye and ruler positioned close to the spring
5. method to determine x: record initial position, record final position and subtraction or record length of stretched spring, original length of spring and subtraction
6. use of a micrometer/calipers to determine diameter d of wire
7. plots a graph of lg x against lg A or equivalent
8. n = gradient and relationship valid if a straight line
9. γ = mgw³N / ρ x 10^(y-intercept)
10. D1 use safety goggles/safety screen to prevent injury to eyes from (moving) spring/load or use cushion/sand box in case load falls
11. D2 keep constant all of: w N ρ (or use same material for wire)
12. D3 measure mass of load/m with a balance or use newton meter to measure weight of load
13. D4 use ruler/calipers to measure the width of the spring/w
14. D5 use the equation ρ = mass of metal / volume to calculate ρ
15. D6 method to measure w, e.g. w measured to the outside and subtract d or method to measure ρ, e.g. mass (balance) and volume (measuring cylinder)
16. D7 repeat measurement of x (for the same A) and average
17. D8 repeat measurements of either d or w made in different places/directions and average
18. D9 use of A = πd²/4 to determine A of wire
19. D10 use of set square to check that clamped ruler is vertical to bench or use of set square/pin as a fiducial mark to read positions (on the ruler)