1. This question is about the flow of liquids.
A student carries out an experiment to investigate how the rate of flow R of water through a narrow tube varies with the pressure difference across the tube. The pressure difference is proportional to the height h shown in the diagram. The student measures h in cm with a metre ruler. R is obtained by measuring the volume of water collected in a measuring cylinder in a time of 100 s.
(a) The student enters the data on a spreadsheet and produces the graph and trend line shown below.
The data point for h=57cm, R=1.70cm3s−1 has not been shown on the graph.The student estimates the uncertainties in all values of h to be ±1 cm and the uncertainties in the values of R to be ±5 %.
(i) On the graph, draw the missing data point.
(ii) On the graph, draw the vertical error bar for this data point.
(iii) Comment on why the trend line is not a perfect match for the data.
(iv) Explain why the student’s estimate of a 5 % uncertainty in all values for R is unlikely to be correct.
(b) The student estimates that the uncertainty in timing 100s is ±1 s. Using the data on the graph, deduce the absolute uncertainty in the volume of water collected when R=2.1cm3s−1.
2. This question is about the forces on a skier.
A skier is pulled up a hill by a rope at a steady velocity. The hill makes an angle of 12° with the horizontal. The mass of the skier and skis is 73 kg. The diagram below shows three of the forces acting on the skier.
(a) On the diagram, draw and label one other force acting on the skier.
(b) Calculate the magnitude of the normal reaction acting on the skier.
(c) The total frictional force acting is 65 N. Determine the tension in the rope.
(d) Explain, using Newton’s first law of motion, why the resultant force on the skier must be zero.
3. This question is about thermal properties of matter.
(a) Explain, in terms of the energy of its molecules, why the temperature of a pure substance does not change during melting.
(b) Three ice cubes at a temperature of 0°C are dropped into a container of water at a temperature of 22 °C. The mass of each ice cube is 25 g and the mass of the water is 330 g. The ice melts, so that the temperature of the water decreases. The thermal capacity of the container is negligible.
(i) Define thermal capacity.
(ii) State the SI unit of thermal capacity.
(iii) The following data are available.
Specific latent heat of fusion of ice = 3.3×105Jkg–1
Specific heat capacity of water = 4.2×103Jkg–1K–1
Calculate the final temperature of the water when all of the ice has melted. Assume that no thermal energy is exchanged between the water and the surroundings.