HW 7 - johnson(mjj622 HW 7 Coker(56625 1 This print-out...

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Unformatted text preview: johnson (mjj622) HW 7 Coker (56625) 1 This print-out should have 18 questions. Multiple-choice 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.

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HW 7 - johnson(mjj622 HW 7 Coker(56625 1 This print-out...

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