1. The diagram below shows part of a downhill ski course which starts at point A, 50 m above level ground. Point B is 20 m above level ground.
(a) A skier of mass 65 kg starts from rest at point A and during the ski course some of the gravitational potential energy transferred to kinetic energy.
(i) From A to B, 24 % of the gravitational potential energy transferred to kinetic energy. Show that the velocity at B is 12 ms-1.
(ii) Some of the gravitational potential energy transferred into internal energy of the skis, slightly increasing their temperature. Distinguish between internal energy and temperature.
(b) (i) The dot on the following diagram represents the skier as she passes point B.Draw and label the vertical forces acting on the skier.
(ii) The hill at point B has a circular shape with a radius of 20 m. Determine whether the skier will lose contact with the ground at point B.
(c) The skier reaches point C with a speed of 8.2 ms-1. She stops after a distance of 24 m at point D.
Determine the coefficient of dynamic friction between the base of the skis and the snow. Assume that the frictional force is constant and that air resistance can be neglected.
(d) At the side of the course flexible safety nets are used. Another skier of mass 76 kg falls normally into the safety net with speed 9.6 ms-1.
(i) Calculate the impulse required from the net to stop the skier and state an appropriate unit for your answer.
(ii) Explain, with reference to change in momentum, why a flexible safety net is less likely to harm the skier than a rigid barrier.
2. (a) Outline what is meant by the principle of superposition of waves.
(b) Red laser light is incident on a double slit with a slit separation of 0.35 mm.A double-slit interference pattern is observed on a screen 2.4 m from the slits.The distance between successive maxima on the screen is 4.7 mm.
Calculate the wavelength of the light. Give your answer to an appropriate number of significant figures.
(c) Explain the change to the appearance of the interference pattern when the red-light laser is replaced by one that emits green light.
(d) One of the slits is now covered.
Describe the appearance of the pattern on the screen.
3. Two renewable energy sources are solar and wind.
(a) Describe the difference between photovoltaic cells and solar heating panels.
(b) A solar farm is made up of photovoltaic cells of area 25000 m2. The average solar intensity falling on the farm is 240 Wm-2 and the average power output of the farm is 1.6 MW. Calculate the efficiency of the photovoltaic cells.
(c) An alternative generation method is the use of wind turbines.
The following data are available:
Length of turbine blade = 17 m
Density of air = 1.3 kg m-3
Average wind speed = 7.5 m s-1
(i) Determine the minimum number of turbines needed to generate the same power as the solar farm.
(ii) Explain two reasons why the number of turbines required is likely to be greater than your answer to (c)(i).