A student measures the spring constant k of a spring using two different methods. The spring constant k of a spring is a measure of the stiffness of the spring. The larger the spring constant k, the more difficult the spring is to stretch.

1. (a)(i)Measure the unstretched length lo of the spring to the nearest 0.1 cm. Do not include the loops at the end of the spring in your measurement. lo = .............................................. cm [1][1]
2. (a)(ii)The student: • attaches the spring to a clamp on a stand • suspends a 300 g mass from the spring. The arrangement of apparatus is shown in Fig. 1.2. The student measures the new length l₁ of the spring. l₁ = 17.6 cm Calculate the extension e of the spring produced by the mass. Use the equation: e = l₁ - lo e = .............................................. cm [1][1]
3. (a)(iii)Calculate the spring constant k₁ of the spring. Use the equation: k₁ = 300 / e k₁ = .............................................. N/m [1][1]
4. (a)(iv)It is important to avoid line-of-sight (parallax) errors when determining the extension of the spring. Explain what is meant by parallax errors and how to avoid parallax errors. explanation ................................................................................................................................................................................................................................................................................ how to avoid parallax errors ................................................................................................................................................................................................................................................................................ [2][2]
5. (b)(i)The student: • pulls the 300 g mass down by a small distance and releases it so that the mass oscillates up and down • measures the time t₁ taken for 20 oscillations. The reading on the stop-watch is shown in Fig. 1.3. Record this time t₁ in Table 1.1 to one decimal place. Table 1.1 mass m/g time t₁ for 20 oscillations/s time t₂ for 20 oscillations/s mean time t for 20 oscillations/s period T/s T²/s² 300 13.8 [1][1]
6. (b)(ii)The student measures the time for 20 oscillations once more and records the time t₂ in Table 1.1. Calculate the mean time t for 20 oscillations and record your answer in Table 1.1. [1][1]
7. (b)(iii)The mean period T of the oscillation is the mean time taken for one oscillation. Calculate the mean period T. Calculate the value of T². Record all your values in Table 1.1. [1][1]
8. (b)(iv)Use your value of T² from Table 1.1 to calculate the spring constant k₂ of the spring. Use the equation: k₂ = 11.8 / T² k₂ = .............................................. N/m [1][1]
9. (c)Explain why the value for the mean period T obtained by measuring 20 oscillations twice is more accurate than the value obtained by measuring 1 oscillation twice. [1][1]

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