1 In this experiment, you will investigate the phase difference between the oscillations of two mass–spring systems.

(a) • Assemble the apparatus as shown in Fig. 1.1. stand boss rod of clamp springs mass B mass A springs rod of clamp boss stand bench mass z Fig. 1.1 • Mass A and mass B are each 200 g. • Add a mass z of 40 g to mass B.

Record the value of z.

z = g • M is given by M = 200 g + z.

Calculate M.

M = g • Pull both A and B down a short distance and release them together. Observe the oscillations. A and B initially oscillate in phase (both moving up and down together), then their oscillations go out of phase and then become in phase again. • The time from A and B oscillating in phase to the next time they oscillate in phase is P.

Measure and record P.

P = [2] , ,

(b) Change z and determine P. Repeat until you have six sets of values of z and P.

Record your results in a table. Include values of M, 1 M and 1 P in your table.

[10]

(c) (i) Plot a graph of 1 P on the y-axis against 1 M on the x-axis. [3]

(ii) Draw the straight line of best fit. [1]

(iii) Determine the gradient and y-intercept of this line.

gradient = y-intercept = [2] , , , ,

(d) It is suggested that the quantities P and M are related by the equation 1 P = M a + b

where a and b are constants.

Use your answers in (c)(iii) to determine the values of a and b.

Give appropriate units.

a = b = [2]

[Total: 20] , , You may not need to use all of the materials provided. , ,

2 In this experiment, you will investigate the tension in a string.

(a) • Set up the apparatus as shown in Fig. 2.1. d ≈ 52 cm ≈ 37 cm ≈ 31 cm bench G-clamp mass hanger and masses string nail bosses nails stand boss Fig. 2.1 • The mass hanger and masses should have a total mass M of 0.400 kg. • The distance between the two lower nails is d, as shown in Fig. 2.1.

Measure and record d.

d = cm [1]

(b) The tension in the string is T.

Calculate T using T = Mg, where g = 9.81 N kg–1.

T = N [1]

(c) (i) • Hook the newton meter on the string half-way between the two lower nails and pull it horizontally with a force F of 5.0 N, as shown in Fig. 2.2. x newton meter Fig. 2.2 • The force F causes the string to deflect a distance x, as shown in Fig. 2.2. Measure and record x.

x = cm [2]

(ii) Estimate the percentage uncertainty in your value of x. Show your working.

percentage uncertainty = % [1] , ,

(iii) Calculate y, where 4 y x d 2 2

e o.

y = cm [1]

(d) • Add slotted masses to the mass hanger so that the total mass M is 0.700 kg. • Repeat (b), (c)(i) and (c)(iii).

T = N

x = cm

y = cm

[3] , ,

(e) It is suggested that the relationship between y, T and x is ky = Tx

where k is a constant.

(i) Using your data, calculate two values of k.

first value of k = second value of k = [1]

(ii) Justify the number of significant figures that you have given for your values of k [1]

(f) It is suggested that the percentage uncertainty in the values of k is 20%.

Using this uncertainty, explain whether your results support the relationship in (e) [1] , ,

(g) (i) Describe four sources of uncertainty or limitations of the procedure for this experiment.

For any uncertainties in measurement that you describe, you should state the quantity being measured and a reason for the uncertainty. 1 2 3 4 [4]

(ii) Describe four improvements that could be made to this experiment. You may suggest the use of other apparatus or different procedures. 1 2 3 4 [4]

[Total: 20] , ,