A system consists of four protons. Three of the protons sit at the corners of an equilateral triangle, and the fourth proton sits at the center of the triangle, as shown in the figure below. Each side of the triangle is 5.10 nm in length. All of the particles in the system are held in place by external forces. Note: the charge of a proton is 1.602×10-19 C, the charge of an electron is -1.602×10-19 C, the mass of a proton is 1.67×10-27 kg, and the mass of an electron is 9.11×10-31 kg. Also, 1 nm is 10-9 m. (a) How much work must be done against electrostatic forces to assemble this system? Note: For this part, you should assume that all particles begin at rest before you start to assemble the system. (b) Suppose that one of the corner protons is released from rest. What maximum speed can the released proton achieve? m/s (c) Suppose we were to replace the proton at the center of the triangle with an electron. What would be the electrostatic potential energy of this new system? (d) How much work must be done against electrostatic forces in order to remove the center proton and replace it with an electron, as described in part (c)?

A system consists of four protons. Three of the protons sit at the corners of an equilateral triangle, and the fourth proton sits at the center of the triangle, as shown in the figure below. Each side of the triangle is 5.10 nm in length. All of the particles in the system are held in place by external forces. Note: the charge of a proton is 1.602×10-19 C, the charge of an electron is -1.602×10-19 C, the mass of a proton is 1.67×10-27 kg, and the mass of an electron is 9.11×10-31 kg. Also, 1 nm is 10-9 m. (a) How much work must be done against electrostatic forces to assemble this system? Note: For this part, you should assume that all particles begin at rest before you start to assemble the system. (b) Suppose that one of the corner protons is released from rest. What maximum speed can the released proton achieve? m/s (c) Suppose we were to replace the proton at the center of the triangle with an electron. What would be the electrostatic potential energy of this new system? (d) How much work must be done against electrostatic forces in order to remove the center proton and replace it with an electron, as described in part (c)?

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter19: Electric Forces And Electric Fields

Section: Chapter Questions

Problem 6P

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Question

Please see the upload images

A system consists of four protons. Three of the protons sit at the corners of an equilateral triangle, and
the fourth proton sits at the center of the triangle, as shown in the figure below. Each side of the triangle
is 5.10 nm in length. All of the particles in the system are held in place by external forces.
Note: the charge of a proton is 1.602×10-19 C, the charge of an electron is -1.602×10-19 C, the mass of
a proton is 1.67×10-27 kg, and the mass of an electron is 9.11×10-31 kg. Also, 1 nm is 10-9 m.
(a) How much work must be done against electrostatic forces to assemble this system? Note: For this
part, you should assume that all particles begin at rest before you start to assemble the system.
(b) Suppose that one of the corner protons is released from rest. What maximum speed can the released
proton achieve?
m/s
(c) Suppose we were to replace the proton at the center of the triangle with an electron. What would be
the electrostatic potential energy of this new system?
(d) How much work must be done against electrostatic forces in order to remove the center proton and
replace it with an electron, as described in part (c)?

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