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Unformatted text preview: johnson (mjj622) HW 7 Coker (56625) 1 This printout should have 18 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. This assignment covers the general defini tion of potential energy for a conservative force, general types of conservation of energy examples (with 2 or more forces doing work), potential energy diagrams, and the concept of binding energy. 001 10.0 points A synthetic rubber band resists being stretched a distance x from equilibrium with a force vector F b ( x ) = bx 2 , where b is a constant. What is the potential energy U b ( x ) associ ated with this elastic band? 1. bx 2 2 2. bx 3 3 3. 2 bx 4. +2 bx 5. + bx 3 3 correct 6. + bx 2 2 7. zero Explanation: By definition U = W . The work we would have to do against the force vector F b to stretch the band is integraldisplay bx 2 dx = bx 3 3 . 002 10.0 points In a certain region of space, a particle expe riences a potential energy U ( x ) = A x 2 + B , where A and B are constants. What force F gives rise to this potential energy? 1. i parenleftbigg A x 2 parenrightbigg 2. i parenleftbigg 2 A x 3 parenrightbigg correct 3. There is no force, since the slope of the line is the constant B A . 4. i parenleftbigg 2 A x 3 parenrightbigg 5. i parenleftbigg A x + B x parenrightbigg 6. i parenleftbigg A x parenrightbigg 7. i parenleftbigg A x + B x parenrightbigg 8. i parenleftbigg A x parenrightbigg 9. i parenleftbigg A x 2 parenrightbigg Explanation: The force is F = dU dx i = i parenleftbigg 2 A x 3 parenrightbigg . 003 10.0 points A block of mass m 1 is attached to a horizon tal spring of force constant k and to a spring of negligible mass. The string runs over a mass less, frictionless pulley to a hanging block of mass m 2 . Initially, the entire system is at rest and the spring is unstretched. johnson (mjj622) HW 7 Coker (56625) 2 m 1 m 2 k m 1 m 2 If mass m 1 slides on a horizontal frictionless surface, what is the speed v of the mass m 2 when it has fallen a distance downward from its rest position? 1. Zero, since the spring will stop it from falling. 2. radicalBigg 2 m 2 g + k 2 m 1 + m 2 3. radicaltp radicalvertex radicalvertex radicalbt m 2 g 1 2 k 2 2 ( m 1 + m 2 ) 4. radicalBigg 2 m 2 g k 2 m 1 + m 2 correct 5. radicaltp radicalvertex radicalvertex radicalbt m 2 g 1 2 k 2 m 1 + m 2 6. radicalBigg 2 m 2 g + k 2 m 1 m 2 7. radicalBigg 2 m 2 g k 2 m 1 m 2 Explanation: Let the gravitational potential energy have a value of 0 at the end state when the system has moved a distance . Applying conserva tion of energy, E = E f U + K = U f + K 1 ,f + K 2 ,f m 2 g + 0 = 1 2 k 2 + 1 2 m 1 v 2 + 1 2 m 2 v 2 2 m 2 g = k 2 + ( m 1 + m 2 ) v 2 2 m 2 g k 2 = ( m 1 + m 2 ) v 2 v 2 = 2 m 2 g k 2 m 1 + m 2 v =...
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This note was uploaded on 02/10/2011 for the course PHY 303K taught by Professor Turner during the Fall '08 term at University of Texas.
 Fall '08
 Turner
 Energy, Potential Energy

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