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chap15_s08_probs

# chap15_s08_probs - Physics 121 Spring 2008 Homework...

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Physics 121 Spring 2008 Homework Problems for Chapter 15 15.3 An alpha particle (charge = +2.0 e ) is sent at high speed toward a gold nucleus (charge = +79 e ). What is the electrical force acting on the alpha particle when it is 2.0 × 10 −14 m from the gold nucleus? ( 29 ( 29 2 2 79 e k e e F r = ( 29 ( 29 ( 29 ( 29 2 19 2 9 2 2 14 158 1.60 10  C N m 8.99 10   91 N   repulsion C 2.0 10  m - - × = × = × 15.5 The nucleus of 8 Be, which consists of 4 protons and 4 neutrons is very unstable and spontaneously decays into two alpha particles (helium nuclei), (a) What is the electric force between two alpha particles when they are 5.00 × 10-15 apart, and (b) what is the acceleration of the alpha particle due to this force ? (a) Applying Coulomb’s law, with q(1) and q(2) = +2e ( 29 ( 29 ( 29 2 19 2 9 2 2 15 2 4 1.60 10 2 N m 8.99 10 36.8 N 2 5.00 10  m k e e F C r - - × = = × = × (b) The mass of an alpha particle = 4.0026 amu (atomic mass units), where 27 u 1.66 10  kg - = × . The acceleration of either alpha particle can be found by applying Newton’s laws: ( 29 27 2 27 36.8 N 5.54 10  m s 4.002 6 1.66 10  kg F a m - = = = × × 15.8 An electron is released a short distance above the surface of the Earth. A second electron directly below it exerts an electrostatic force on the first electron which just cancels the gravitational force due to Earth. What is the separation of these two electrons ? This problem describes an electric balancing act. The magnitude of the repulsive force between these two electrons must equal the weight of an electron,

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Thus, 2 2 e e k e r m g = - electric force = gravitational force. Note that m e g = 2 R M m G Earth e , because “little g” is the gravitational acceleration of the Earth. or ( 29 ( 29 ( 29 ( 29 2 9 2 2 19 2 31 2 8.99 10   N m C 1.60 10  C 5.08 m 9.11 10  kg 9.80 m s e e k e r m g - - × × = = = × 15.10 Calculate the magnitude and direction of the Coulomb force on each of the three charges shown in this figure. There are two positive and one negative charge.
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chap15_s08_probs - Physics 121 Spring 2008 Homework...

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