Maximum Kinetic Energy - General Physics - Past Paper, Exams of Physics

Download Maximum Kinetic Energy - General Physics - Past Paper and more Exams Physics in PDF only on Docsity! Physics 2101, Final Exam, Spring 2008 May 8, 2008 Name: Section: (Circle one) 1 (Rupnik, MWF 8:40am) 2 (Giammanco, MWF 10:40am) 3 (González, MWF 12:40pm) 4 (Rupnik, MWF 2:40pm) 5 (Rupnik, TTh 9:10am) 6 (Sheehy, TTh 12:10pm) • Please be sure to write your name and circle your section above. • For the questions, no work needs to be shown (there is no partial credit). • Please carry units through your calculations when needed, lack of units will result in a loss of points. • You may use scientific or graphing calculators, but you must derive your answer and explain your work. • Feel free to detach, use and keep the formula sheet. No other reference material is allowed during the exam. • For the problems, explain your reasoning as much as possible. Partial credit will be awarded, and correct answers with no work shown will not receive full credit. • GOOD LUCK! 1 Question 1 (7 pts): The figure shows a plot of potential energy versus position U(x) of a conservative force F (x). A particle is at point x = b at t = 0, moving towards the left. It temporarily stops when it reaches x = a, and then it begins moving towards the right. (a) (3pts) What is the maximum kinetic energy that the particle will have ? 0 U(a) U(b) U(a)− U(b) U(c) U(d) (b) (2pts) Will the particle ever reach point d? Yes No We need more information to decide. (c) (2pts) What are the turning points for this particle’s motion? a, b, c a, c a, c, f b, d, e 2 Problem 1(13pts): A uniform beam of length L is supported by a cable perpendicular to the beam and a hinge at angle θ. The tension in the cable is T . Express your answers to the following questions in terms of T, g, L, θ and numerical constants as needed. (a) (3pts) Next to the figure, draw a free body diagram for the beam. (b) (3pts) What is the mass of the beam? (c) (4pts) What is the force of the hinge on the beam?Write an expressions for the magnitude of the horizontal and vertical components of the hinge force. (d) (3pts) The cable snaps. Just after the cable snaps, what is the magnitude of the angular acceleration of the beam about the hinge? 5 Problem 2 (12pts): A solid disk of mass M = 1.5 kg and radius R = 0.10 m is hanging from a massless thin rod of length D = 1.2 m. (a) (2 pts) What is the rotational inertia of the disk-rod system with respect to the attachment point P? x y s P ? 6 D mp p p - ~v◦ &% '$ M, R ? 6h 1 (b) (3 pts) A bullet with mass m = 20.0 g is fired horizontally towards the center of mass of the disk with a speed of v0 = 500 m/s. In unit vector notation, what is the angular momentum ~L of the bullet with respect to point P just before it collides with the disk? Use the coordinate system with axes as shown in the figure, with the z-axis out of the page. (c) (4 pts) After the very short collision, the bullet gets embedded in the disk. In unit vector notation, what is the angular velocity ~ω of the thin rod-bullet-disk system just after the collision? (d) (3 pts) Find the distance h to which the center of mass of the disk-bullet system swings after the collision. 6 Problem 3 (12 pts): Three spheres with the same mass M are placed in the positions shown in the figure, with spheres B and C on the x-axis, and sphere A on the y axis, at a distance D from the origin. Express your answer to the following questions in terms of M,D, Newton’s constant G and numerical constants as needed. (a) (5 pts) In unit-vector notation, what is the gravitational force on A due to B and C? (b) (5 pts) What is the total gravitational potential energy stored in the system? Assume U = 0 at infinity. (c) (2 pts) Initially, all spheres were at rest at an infinite distance; you brought them one by one and set them at the positions shown in the figure, again at rest. What is the total work done by you to assemble the system? 7 Problem 4 (12pts) : A 40g piece of ice is taken from the freezer at −15.0◦C, and dropped in to 200g of water in a thermally insulated container, initially at 25.0◦C. After a while, the system reaches an equilibrium temperature Tf > 0◦. (a) (3pts) What is the heat absorbed by the ice after it warmed up to 0◦C? (b) (3pts) What is the heat absorbed by the ice to completely melt at T = 0◦C? (c) (3pts) What would be the heat released by the water if it had cooled down to freezing temperature, 0◦C? (d) (3pts) What is the actual final equilibrium temperature Tf? 10 Question 6 (7pts) : In the p-V diagram shown in the figure, an ideal gas undergoes an isothermal expansion, then a pressure reduction at constant volume, and finally an adiabatic compression to the initial volume. (a) (2pts) In which of the three processes is the gas absorbing heat? 1→ 2 2→ 3 3→ 1 All of them None of them (b) (3pts) In which of the three processes is the gas decreasing entropy? 1→ 2 2→ 3 3→ 1 All of them None of them (c) (2pts) The cycle 1→ 2→ 3→ 1 is a ... a heat engine a refrigerator neither a heat engine nor a refrigerator 11 Problem 5 (12 pts): In the p-V diagram shown in the figure, two moles of an ideal diatomic gas undergo the processes shown in the figure. The initial pressure and temperature at point 1 are p1 = 1atm and T1 = 300K. (a) (4pts) What is the initial volume, at point 1? (b) (4 pts) What are the pressure and temperature at point 3? (c) (4 pts) What are the work done by the gas and the change in internal energy of the gas in the process 3→ 1? 12