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Test #3-solutions - Version 100/ABCBA Test#3...

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Version 100/ABCBA – Test #3 – Antoniewicz – (56445) 1 This print-out should have 22 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points The potential energy U ( r ) between any two atoms, when given as a function of the dis- tance between their centers, will have a form similar to the graph below. U ( r ) r 0 E 3 E 2 E 1 For which possible total energy of the two atoms, as shown in the sketch, do the atoms behave most like a simple harmonic oscillator? 1. E 3 2. They behave like a SHO for any energy. 3. There is no energy for which the two atoms will behave in any way even vaguely like a SHO. 4. E 1 correct 5. E 2 Explanation: Since a SHO potential energy would be pro- portional to ( r - r 0 ) 2 , where r 0 is a constant, we would expect U ( r ) to be most like a SHM at the energy E 1 . Therefore, for the lowest energy, E 1 , the potential energy is most like that of a simple harmonic oscillator. 002 10.0 points The force due to a deflected cantilever beam can be modeled using a linear and cubic term, i.e. F beam = - k 1 δ - k 3 δ 3 where δ is the deflection at the end of the beam. What work must be done on the beam to deflect it by 16 cm if k 1 = 97 N / m and k 3 = 20000 N / m 3 ? 1. 2.92793 2. 17.2955 3. 4.5184 4. 3.10219 5. 16.6635 6. 7.15522 7. 5.6066 8. 5.7024 9. 25.9246 10. 20.3996 Correct answer: 4 . 5184 J. Explanation: The work done on the beam is given by W on beam = - W by beam = - δ max 0 F beam d δ = δ max 0 k 1 δ + k 3 δ 3 d δ = 1 2 k 1 δ 2 + 1 4 k 3 δ 4 δ max 0 = 4 . 5184 J 003 10.0 points The figure shows a potential energy curve for the interaction of a two atom system. The horizontal line represents a bound state with constant K+U value.
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Version 100/ABCBA – Test #3 – Antoniewicz – (56445) 2 What is the minimum amount of energy (in units of eV) which must be supplied to cause the separation of two atoms? (Caution: be careful with the sign here.) 1. 0.2 correct 2. -1.2 3. -0.9 4. -0.2 5. 1.3 6. 0.9 Explanation: The minimum amount of energy needed is to bring the system from present state where E i = ( K + U ) i = - 0 . 2 eV to the final state where E f = ( K + U ) f = 0. The energy principle is E f - E i = W Δ E = W = E f - E i = 0 - ( - 0 . 2 eV) = 0 . 2 eV . 004 10.0 points The escape speed from an asteroid whose ra- dius is 20 km is only 6 m / s. If you throw a rock away from the asteroid at a speed of 12 m / s, what will be its final speed? Use G = 6 . 7 × 10 - 11 N · m 2 / kg 2 . 1. 10.3923 2. 12.1244 3. 22.5167 4. 17.3205 5. 20.7846 6. 25.9808 7. 15.5885 8. 13.8564 9. 19.0526 10. 24.2487 Correct answer: 10 . 3923 m / s. Explanation: First use the escape speed to get the mass of the asteroid: v esc = 2 G M R M = 1 2 v 2 R G = 5 . 37313 × 10 15 kg . Now, if v i = 12 m / s, then v f is found from E i = E f : U i + K i = U f + K f ⇒ - G M m r i + 1 2 m v 2 i = 0 + 1 2 m v 2 f v f = v 2 i - 2 G M R = 10 . 3923 m / s . 005 10.0 points Which of the following is a physical feature of a real spring which is NOT represented by the ideal spring potential energy graph, U ideal = 1 2 k s s 2 - E S ?
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