Final_Exam_solution-Sp03

# Final_Exam_solution-Sp03 - Physics 221 Final Exam Spring...

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Physics 221. Final Exam Spring 2003 The situation below refers to the next two questions: A block of mass m = 0 . 2 kg starts from rest at point A and slides down a frictionless curved surface to point B, where its speed is v = 8 m/s. Then, it slides along a rough horizontal surface for d =10 m and comes to rest at point C. A h B C d 1. What is the initial height h of the block? a. h = 1.2 m b. h = 2.5 m *c. h = 3.3 m d. h = 4.6 m e. h = 5.1 m Mechanical energy is conserved while no friction is present: 2 2 1 00 2 3.3 2 +=+ == mgh mv v hm g 2. Find the coefficient of kinetic friction between the block and the horizontal surface between B and C . a. μ k = 0 . 1 b. μ k = 0 . 2 *c. μ k = 0 . 3 d. μ k = 0 . 4 e. μ k = 0 . 5 The missing mechanical energy must be equal to the work done by friction: 2 2 1 0 2 0.3 2 non conservative k kk k k EW mv f d v where f N mg gd µµ µ ∆= −= ⇒ == Page 1 of 28

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Physics 221. Final Exam Spring 2003 The situation below refers to the next two questions: The graph below shows the potential energy U and the total mechanical energy E of a particle as a function of position x . The only force acting on this particle is the force associated to this potential energy. U (J) E = 5.0 J x (m) 1 2 3 4 5 6 3. At which position does the particle have the greatest kinetic energy? a. At x = 1 m b. At x = 2 m *c. At x = 4 m d. At x = 5 m e. At x = 6 m Max KE Min U At x = 4 m 4. Which of the following statements about the force on the particle at x = 3 m is true? a. It is zero b. It points in the x direction *c. It points in the + x direction d. The particle can never be at x = 3 m, so there is no force to be discussed. e. The direction of the force depends on the direction of the velocity of the particle. The force is minus the slope of the U(x) curve, x dU F dx =− . At x = 3 m, the curve has a negative slope, so the force must point in the +x direction. Page 2 of 28
Physics 221. Final Exam Spring 2003 The situation below refers to the next two questions: A rope is attached to the handle of a bucket with a stone of mass m inside. A person swirls the whole system in vertical circles as shown in the figure below. The distance between the stone and the center of the circle is L = 1.5 m. L 5. What is the minimum speed that the system must have at the highest point of the trajectory if the stone is to stay in contact with the bottom of the bucket? *a. v min = 3.8 m/s b. v min = 4.2 m/s c. v min = 5.7 m/s d. v min = 6.1 m/s e. v min = 7.8 m/s The condition for minimum speed is that the normal force exerted by the bottom of the bucket on the stone is equal to zero when the system is at the highest point of the trajectory. This means that the only force providing the required centripetal acceleration to the stone is its weight mg. 2 min min 3.8 / v mg m L vg Lm = == s 6. As the bucket moves from the highest to the lowest point in its trajectory, the work done by the tension on the rope is ________ and the work done by gravity is ________.

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Final_Exam_solution-Sp03 - Physics 221 Final Exam Spring...

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