In this experiment you will measure 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. You are provided with: • a spring • a boss, clamp and stand • a 30 cm ruler • a stop-watch • a 300 g mass.

1. (a)Method 1
2. (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]
3. (a)(ii)Attach the spring to the clamp and suspend the 300 g mass from the spring, as shown in Fig. 1.1. [Figure 1.1] Measure and record the new length l₁ of the spring. Calculate the extension e of the spring produced by the mass. Use the equation: e = l₁ - lo l₁ = .............................................. cm e = .............................................. cm [1][1]
4. (a)(iii)Calculate the spring constant k₁ of the spring. Use the equation: k₁ = 300/e k₁ = .............................................. N/m [1][1]
5. (a)(iv)It is important to avoid line-of-sight (parallax) errors when determining the extension of the spring. Describe how you avoid parallax errors. ......................................................................................................................................................... ......................................................................................................................................................... [1][1]
6. (b)Method 2 • Pull the 300 g mass down a small distance (about 2 cm) and release it. • Observe that the mass oscillates up and down. • Stop the mass oscillating. • Pull the 300 g mass down a small distance again and release it.
7. (b)(i)Measure the time t₁ taken for 20 oscillations. Record this time in Table 1.1. Repeat the measurement. Record this time in Table 1.1 as t₂. [2] 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 mean period T/s T²/s² 300[2]
8. (b)(ii)Calculate the mean time t for 20 oscillations and record your answer in Table 1.1. [1][1]
9. (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]
10. (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]
11. (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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