PHYS 217 Final, Fall 2018

IS fa / N Find the atomic mass 0 Physics 217 Final examination, Dec 12, 2018. Time: 2 hours thirty minutes. Open book examination. Choose six out of the seven questions below. é When a mass of 0.5 kg is suspended from a spring, the length of the spring is extended by 50 mm. a. What is the spring constant? b. What is the frequency of oscillation if the mass is given an impulse upwards? c. If this impulse gives it a velocity of 20 cm/seq find the amplitude of the resulting oscillation| Write an expression for the position as a function of time for such oscillations. Q) A particle is subjected to a force of the form F= -kx + c/x’. a. What is the potential describing such a force? b. What is the position of equilibrium? c. What is the period of small oscillations about that point? 3.) A meteorite of mass 50 Kg. is approaching the earth at a velocity of 2000 m/sec. its closest distance of approach is 500 km from the surface of the earth. *, . . —._ *. a. What are its kinetic energy and its angular momentum? b. What is its impact parameter? ter. It has radius R= 30 (4) A circular disc has a uniform mass density p = 100 grams/cubic centime pram abic cent cm and thickness of 1 cm. Calculate its three principlemoments ofinertia. ar dmr-r fee C av-du- a. ree prit b. The same density material is used to make a cone of height 30 cm and base of radius 30 cm. Calculate its (moment of inertia about its axis of symmetry. What is its kinetic energy if it is ‘\\ made to spin at an angular velocity of 100 revolutions per second. A bird of mass 2 kg is flying at a speed of 10m/sec in latitude 60° north heading due east. Find the ontal and vertical components of the Coriolis force acting on it. . Dory e<b Ke A Roms} / (6p proton is ¢fastically scattered through an angle of 56° by a nucleus which recoils at an angle of 60°. f the nucleus and the fraction of kinetic energy transferred to it. " i eachiniatalioc iashl-) Balashdiah aici horiz eo C, A pendulum is hanging from a fixed ceiling. The pendulum swings underneath in two directions. Use the two angles of the position of the pendulum to write the Lagrange function of the system. a. Find the equations of motion. b. Write the Hamiltonian and the Hamilton equations of motion. If M= 3kg, and is at rest , m= 1kg. and l= 2m and the pendulum is released at an angle of 30° from the vertical with horizontal velocity of 20 m/sec. Find the energy and angular momentum of the system. c. ye x te