1. A girl on a sledge is moving down a snow slope at a uniform speed.
(a) Draw the free-body diagram for the sledge at the position shown on the snow slope.
(b) After leaving the snow slope, the girl on the sledge moves over a horizontal region of snow. Explain, with reference to the physical origin of the forces, why the vertical forces on the girl must be in equilibrium as she moves over the horizontal region.
(c) When the sledge is moving on the horizontal region of the snow, the girl jumps off the sledge. The girl has no horizontal velocity after the jump. The velocity of the sledge immediately after the girl jumps off is 4.2 ms–1. The mass of the girl is 55 kg and the mass of the sledge is 5.5 kg. Calculate the speed of the sledge immediately before the girl jumps from it.
(d) The girl chooses to jump so that she lands on loosely-packed snow rather than frozen ice. Outline why she chooses to land on the snow.
(e) The sledge, without the girl on it, now travels up a snow slope that makes an angle of 6.5˚ to the horizontal. At the start of the slope, the speed of the sledge is 4.2 ms–1.The coefficient of dynamic friction of the sledge on the snow is 0.11.
(i) Show that the acceleration of the sledge is about –2 ms–2.
(ii) Calculate the distance along the slope at which the sledge stops moving.Assume that the coefficient of dynamic friction is constant.
(f) The coefficient of static friction between the sledge and the snow is 0.14. Outline, with a calculation, the subsequent motion of the sledge.
2. The Feynman diagram shows electron capture.
(a) Deduce that X must be an electron neutrino.
(b) Distinguish between hadrons and leptons.
3. Electrical resistors can be made by forming a thin film of carbon on a layer of an insulating material.
(a) A carbon film resistor is made from a film of width 8.0 mm and of thickness 2.0 μm.The diagram shows the direction of charge flow through the resistor.
(i) The resistance of the carbon film is 82 Ω. The resistivity of carbon is 4.1*10–5 Ω m. Calculate the length l of the film.
(ii) The film must dissipate a power less than 1500 W from each square metre of its surface to avoid damage. Calculate the maximum allowable current for the resistor.
(iii) State why knowledge of quantities such as resistivity is useful to scientists.