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Physics: answer two questions

7.

Explain what are meant by the terms linear momentum and kinetic energy. [3] It is often easier to make calculations involving collisions in the zero momentum frame. Explain what this is and why its use helps simplify such calculations. [3] A mass m travelling at speed u through the laboratory makes a head-on collision with a mass M travelling at speed v in the opposite direction. The two masses stick together after the collision. Show that the change in the kinetic energy is the same when calculated in the laboratory frame as it is when calculated in the zero-momentum frame. [9]

8.

Write down Kirchoff's circuit laws.

[3]

An inductance, L, and a resistance, R, are connected in series with a switch and a battery of voltage V. The switch is initially open, but is closed at time t = 0. (a) Write down a differential equation describing the current in the circuit for times t t 0. [4] (b) Given that the current obeys the equation I = I0 [1 exp(t /W )], find expressions for I0 and W in terms of R, L, and V. [4] (c) Make a labelled sketch of the variation of I as a function of t for t t 0 [4]

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9.

The time taken for 10 full swings of a long pendulum performing small angle oscillations is measured seven times. The results (in seconds) are: 34.63, 34.80, 34.71, 34.80, 38.21, 34.54, 34.77 (a) Estimate the error in making a timing measurement. [3] (b) Estimate of the period of the pendulum and the error in this estimate. [3] The pendulum is now left to swing and two experiments are made in which the time is measured for many complete swings using the same method as for one swing. The measured times in two such experiments are 340.41 s and 1059.88 seconds. Use the method of exact fractions for each of these experiments in turn, calculate two successively better estimates of the period of the pendulum. On the assumption that that the error in the timing measurement is the same as you calculated in (a), what is the error in your best estimate of the period? [6] The period of the pendulum, T, the length of the pendulum, l, and the gravitational field strength, g, are related by g = 4 2l /T2. If the length of the pendulum is known perfectly, with what percentage error could you estimate g from your results? [3]

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