20 18 The photographs show a wooden pop gun before and after the cork is popped. The diagram shows a cross-section through the pop gun. wooden cylinder handle air piston cylindrical cork Initially the piston is at the right-hand end of the cylinder, as shown. Then the cork is pushed into the other end of the cylinder. When the handle is pushed in, the pressure of the air in the cylinder increases. This exerts an additional force on the cork. Once the additional force is sufficient to overcome the frictional force between the cork and the cylinder, the cork is pushed out. (a) Show that the pressure of the air in the cylinder must be about 2 × 105 Pa in order to push the cork out. maximum frictional force = 8.8 N cross-sectional area of cork = 9.2 × 10−5 m2 atmospheric pressure = 1.0 × 105 Pa (3) .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. .................................................................................................................................................................................................................................................. Turn over 21 (b) Calculate the temperature of the gas in the cylinder at the instant the cork is expelled. volume of air in the cylinder with the handle pulled out = 1.1 × 10−5 m3 volume of air in the cylinder at the moment the cork is pushed out = 6.7 × 10−6 m3 atmospheric pressure = 1.0 × 105 Pa initial temperature of air = 19 °C (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Temperature = .................................................................... (c) The formulae sheet for this paper includes the equation pV = 1 3 Nm〈c2〉 Derive the equation 1 2 m〈c2〉 = 3 2 kT (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... (d) Calculate the root mean square speed of the molecules of air in the cylinder before the handle is pushed in. average mass of molecule of air = 4.8 × 10−26 kg temperature of air = 19 °C (2) ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... ................................................................................................................................................................................................................................................... Root mean square speed = .................................................................... (Total for Question 18 = 9 marks)