1. Data analysis question.
Connie and Sophie investigate the effect of colour on heat absorption. They make grey paint by mixing black and white paint in different ratios. Five identical tin cans are painted in five different shades of grey.
Connie and Sophie put an equal amount of water at the same initial temperature into each can. They leave the cans under a heat lamp at equal distances from the lamp. They measure the temperature increase of the water, T, in each can after one hour.
(a) Connie suggests that T is proportional to B, where B is the percentage of black in the paint. To test this hypothesis, she plots a graph of T against B, as shown on the axes below. The uncertainty in T is shown and the uncertainty in B is negligible.
(i) State the value of the absolute uncertainty in T.
(ii) Comment on the fractional uncertainty for the measurement of T for B= 10 and the measurement of T for B= 90.
(iii) On the graph opposite, draw a best-fit line for the data.
(iv) Outline why the data do not support the hypothesis that T is proportional to B.
(b) Sophie suggests that the relationship between T and B is of the form
T = kB1/2 + c
where k and c are constants.
To test whether or not the data support this relationship, a graph of T against B1/2 is plotted as shown below. The uncertainty in T is shown and the uncertainty in B1/2 is negligible.
(i) Use the graph to determine the value of c with its uncertainty.
(ii) State the unit of k.
2.This question is about a tidal power station.
A tidal power station is built for a coastal town. Sea water is stored in a tidal basin behind a dam at high tide and released in a controlled manner between high tides, so that it passes through turbines to generate electricity.
(a) (i) Show that the mass of sea water released between successive high and low tides is about 2.8×108 kg.
(ii) Calculate the electrical energy produced between successive high and low tides.
(b) (i) Identify one mechanism through which energy is transferred to the surroundings during the electricity generation process.
(ii) State why the energy transferred to the surroundings is said to be degraded.
3. This question is about electric and magnetic fields.
A proton travelling to the right with horizontal speed 1.6×104 ms–1 enters a uniform electric field of strength E. The electric field has magnitude 2.0×103 NC–1 and is directed downwards.
(a) Calculate the magnitude of the electric force acting on the proton when it is in the electric field.
(b) A uniform magnetic field is applied in the same region as the electric field. A second proton enters the field region with the same velocity as the proton in (a). This second proton continues to move horizontally.
(i) Determine the magnitude and direction of the magnetic field.
(ii) An alpha particle enters the field region at the same point as the second proton, moving with the same velocity. Explain whether or not the alpha particle will move in a straight line.