26 10 A spring is made from loops of thick steel wire as shown. w There are two extra loops, one on each end of the spring. (a) A student determined the length of steel used to make the spring by using vernier calipers to measure the width w of the spring. The length of wire l on each loop is given by l = πw The student obtained the following values for w. w / mm 15.3 15.2 15.4 15.3 (i) Calculate l. (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. l = ....................................................... (ii) Estimate the percentage uncertainty in your value for l. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. % uncertainty in l = ....................................................... 27 (iii) Calculate the total length L of wire used to make the spring. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. L = ....................................................... (b) The student measured the diameter d of the steel wire and obtained a value of 2.52 mm. (i) Explain which instrument he used to measure the diameter. (2) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (ii) Estimate the percentage uncertainty in the student’s value for d. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. % uncertainty in d = ....................................................... (iii) The student used a balance to measure the mass m of the spring. He obtained a value of 32.0 ± 0.5 g. Estimate the percentage uncertainty in the mass of the spring. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. % uncertainty in m = ....................................................... (iv) The student calculated the density ρ of the steel using the equation ρ m V Calculate the percentage uncertainty in his value for the density of steel. (1) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. % uncertainty in value for density of steel = ....................................................... Turn over 28 (v) Determine whether the data collected leads to a value for the density of steel in agreement with the standard value. density of steel = 7 800 kg m−3 (4) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. (Total for Question 10 = 16 marks) 29 Turn over BLANK PAGE