Question

1(c) In a laboratory experiment to determine the force constant of a spiral spring, the mass on the spring was varied and the corresponding extensions were measured and recorded as shown in the table below.
Mass(g): 50,100,150,200,250 | Weight W/N: (to calculate) | Extension e/cm: 6.5, 11.0, 15.0, 20.0, 25.0
(i) Copy and complete the table (Take g = 10 ms⁻²) (ii) Plot a graph of weight, W, on the vertical axis and extension, e, on the horizontal axis. (iii) Using the graph, determine the force constant of the spring. (iv) Determine the natural length of the spring if its length was 38.0 cm when loaded with 250 g mass.

Accepted Answer

(i) Weight W(N) = mass(kg) x g: 0.5, 1.0, 1.5, 2.0, 2.5 N for masses 50g-250g respectively; extension e/m: 6.5x10⁻², 11.0x10⁻², 15.0x10⁻², 20.0x10⁻², 25.0x10⁻² m.
(iii) Slope = ΔW/Δe = (W2-W1)/(e2-e1) = (2-0.65)/(20-6.5)x10⁻² = 1.35/13.5x10⁻² = 10 N/m. This slope is the force constant k = 10 N/m.
(iv) Extension = final length - original length. When loaded with 250g, extension = 25cm and final length = 38.0cm. Natural (original) length = final length - extension = 38 - 25 = 13cm.

WAEC Physics 2011 Theory — Question 3

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