1.1. A student is determining the spring constant k of a spring by two methods.

Fig. 1.2 shows how the apparatus is used.

Method 1

On Fig. 1.1, measure the unstretched length ${l}_{0}$ of the spring, in mm.

${l}_{0}$ = ................................................. mm 

1.2. Extended tier only

The student attaches the spring to the clamp as shown in Fig. 1.2.

He hangs a 300 g mass on the spring.

He measures the new length $l$ of the spring.

$l$ = 53 mm

(i) Calculate the extension e of the spring using the equation $e=l-{l}_{0}$.        

e = ................................................. mm [1]

(ii) Calculate a value for the spring constant k using the following equation:  

$k=\frac{F}{e}$ ,

where F = 3.0 N.        

k = ............................................ N/mm [1]

1.3. Method 2

The student pulls the mass down a short distance and releases it so that it oscillates up and down. Fig. 1.3 shows the time t taken for 10 complete oscillations.

(i) Record the time t taken for 10 complete oscillations.

 t = ........................................................ [1]

(ii)

1. Calculate the time T taken for one complete oscillation.

T = .............................................................

 2. Calculate T ².

   T ² = .............................................................

[2]

(iii) Calculate the spring constant k using the following equation:

$k=\frac{0.040m}{{T}^{2}}$,

where m = 0.300kg.

   k = ............................................ N/mm [1]

1.4. State and explain whether your two values for k are the same within the limits of experimental accuracy.

1.5. A student states that repeating Method 1 with different masses would improve the reliability of the value obtained for k.

Suggest additional values for the mass m that you would use when repeating the experiment to improve the reliability.