1. Data analysis question.

An experiment is undertaken to investigate the relationship between the temperature of a ball and the height of its first bounce.

A ball is placed in a beaker of water until the ball and the water are at the same temperature. The ball is released from a height of 1.00 m above a bench. The maximum vertical height h from the bottom of the ball above the bench is measured for the first bounce. This procedure is repeated twice and an average hmean is calculated from the three measurements.

The procedure is repeated for a range of temperatures. The graph shows the variation of hmean with temperature T.

(a) Draw the line of best-fit for the data.

(b) State why the line of best-fit suggests that hmean is not proportional to T.

(c) (i) State the uncertainty in each value of T.

(ii) The temperature is measured using a liquid in glass thermometer. State what physical characteristic of the thermometer suggests that the change in the liquid’s length is proportional to the change in temperature.

(d) Another hypothesis is that hmean=KT3 where K is a constant. Using the graph on page 2, calculate the absolute uncertainty in K corresponding to T=50°C.


2. This question is about gravitation and uniform circular motion.

Phobos, a moon of Mars, has an orbital period of 7.7 hours and an orbital radius of 9.4×103 km.

(a) Outline why Phobos moves with uniform circular motion.

(b) Show that the orbital speed of Phobos is about 2kms–1.

(c) Deduce the mass of Mars.


3. This question is about simple harmonic motion (SHM).

The graph shows the variation with time t of the acceleration a of an object X undergoing simple harmonic motion (SHM).

(a) Define simple harmonic motion (SHM).

(b) X has a mass of 0.28 kg. Calculate the maximum force acting on X.

(c) Determine the maximum displacement of X. Give your answer to an appropriate number of significant figures.

(d) A second object Y oscillates with the same frequency as X but with a phase difference of π/4. Sketch, using the graph opposite, how the acceleration of object Y varies with t.




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