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Unformatted text preview: PHY6938 Proﬁciency Exam Fall 2002 September 13, 2002 Mechaincs
1. The system (Atwood’s machine) shown in the ﬁgure consists of two masses, m1 and m2 , attached to the ends of a string of length l which hangs over a pulley. The pulley is a uniform disk of radius r and mass m. Assume the string is massless and does not slip on the pulley. (a) What is the moment of inertia of the pulley about its axis ? (Perform a calculation to determine I ; do not just write down a remembered answer.) (b) Obtain the acceleration of the masses. (c) Find the tension of the string on both sides of the pulley. (d) Write down an expression for the total energy of the system. 2. A wedge of mass M = 4.5 kg sits on a horizontal surface. Another mass m = 2.3kg sits on the sloping side of the wedge. the incline is at an angle of 31.7◦ with respect to the horizontal. All surfaces are frictionless. The mass m is released from rest on mass M , which is also initially at rest. What are the accelerations of M and m once the mass is released ? ¢¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¢¡¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢ ¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡¡ m r g m2 m1 m g M θ
3. A single-stage rocket of initial mass m0 is launched vertically at constant burn rate of the fuel α. The payload mass of the rocket is mF . The gas is exhausted at a constant speed u relative to the rocket. Neglect air resistance and assume that the acceleration of gravity is constant with height. (a) Derive an expression for the velocity as a function of mass of the rocket. (b) Calculate the time tb at which the fuel is burnt out. (c) For the ﬁrst stage of a Saturn V rocket for the Apollo moon program, the initial mass is m0 = 2.8 × 106 kg, mF = 7 × 105 kg, u = 2600m/s and assume a mean thrust of 37 × 106 N. Obtain the ﬁnal speed at burnout and the burnout time tb . ...
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This note was uploaded on 03/11/2012 for the course PHY 3900 taught by Professor Staff during the Fall '1 term at FSU.
- Fall '1