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PHYSICS Part IA Wednesday 19 January 2009 SELWYN COLLEGE REVISION TEST

Attempt all three questions from section A and any two from section B.

SECTION A ­ answer all questions. A1 A physicist measures two dimensionless quantities and reports the following numerical values: A = 10 ±1 and B = 5±2. Calculate C = A x B2 and estimate its uncertainty, noting any assumptions which you make. [5] Assuming that you can jump a maximum of 1 metre into the air on earth, calculate the largest radius of a homogeneous spherical asteroid from which you could jump clear. (Assume a density of 3000 kg m-3 for the asteroid.) [5] The highest energy cosmic rays have energies E=1020 eV. One of these, assumed to be a proton, enters the atmosphere at an altitude of 20km. In the frame of reference of the proton, how long would it take to pass through the atmosphere, assuming it suffers no collisions? [5]

A2

A3


SECTION B ­ answer two questions B4. Explain what is meant by the term energy, illustrating your answer with two examples of potential energy and two of kinetic energy. [5] A uniform solid cylinder rolls from rest without slipping down a rough inclined plane, then along a horizontal section where the surface texture changes from rough to smooth, and finally up a second inclined plane with a perfectly-smooth surface. By considering changes in energy show that, if the cylinder drops a height h on its way down the first inclined plane and rises to a maximum height y on the second inclined plane, then h and y are related by y= ma 2 h, ma 2 + I

where I is the moment of inertia of the cylinder, m its mass, and a its radius. [6] Calculate the ratio of y/h for (a) a solid cylinder, and (b) a thin-walled hollow open-ended cylinder. [4] B5. A mass m is moving in a straight line through the laboratory at relativistic speed u when it collides head-on with another stationary mass m. The two masses interact and form a single larger mass M. (a) Explain carefully what are meant by the terms energy, momentum, and kinetic energy in this context, and write down expressions for the total energy and total momentum both before and after the collision in the laboratory frame. [7] (b) By using the relativistic invariant E2 ­ p2c2, or otherwise, show that, if M = 4m, then the value of of the moving mass before the collision is at least 7. [8] B6. Write down Kepler's three laws of planetary motion. An astronaut is at the top of a tower asteroid of uniform density, mass M, at just such a speed, u, that it just before hitting him in the back. Show [6]

of height h above the surface of a spherical and radius R. He throws a ball horizontally misses grazing the surface of the asteroid that u is given approximately by


u= where G is the gravitational constant.

GM 3h ) , 1 - R 4R [9]