An electron and a proton are both in motion near each other as shown in the figure below; at this instant they are a distance r apart. Theproton is moving with speed up at an angle to the horizontal, and the electron is moving straight up with speed ve. (Assume the +xdirection is to the right and the +y direction is upward. Indicate the direction with the sign of your answer.)Proton8VpElectron

Step 1:Force Components from Proton to Electron Electric Field due to the Proton at the Location of…

Answered: An electron and a proton are both in…

College Physics

10th Edition

ISBN:9781285737027

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter26: Relativity

Section: Chapter Questions

Problem 17P

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The mass of a theoretical particle that may be associated with the uni?cation of the electroweak and strong forces is (a) How many proton masses is this? (b) How many electron masses is this? (This indicates how extremely relativistic the accelerator would have to be in order to make the particle, and how large the relativistic quantity (would have to be.)
Electrons in projection television sets are accelerated through a total potential difference of 50,000 V. (a) Calculate the speed of the electrons using the relativistic form of kinetic energy assuming the electrons start from rest. (b) Calculate the speed of the electrons using the classical form of kinetic energy. (c) Is the difference in speed significant in the design of this set in your opinion?
A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet, they annihilate, converting all of their mass into energy. (a) Find the energy released, assuming negligible kinetic energy before the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity? (c) If this energy is given to another electron in the form of kinetic energy, what is its velocity?
A Van de Graaff accelerator utilizes a 50.0 MV potential difference to accelerate charged particles such as protons. (a) What is the velocity of a proton accelerated by such a potential? (b) An electron?
(a) Beta decay is nuclear decay in which an electron is emitted. If the electron is given 0.750 MeV of kinetic energy, what is its velocity? (b) Comment on how the high velocity is consistent with the kinetic energy as it compares to the rest mass energy of the electron.
A chain of nuclear reactions in the Suns core converts four protons into a helium nucleus. (a) What is the mass difference between four protons and a helium nucleus? (b) How much energy in MeV is released during the conversion of four protons into a helium nucleus?
The creation and study of new and very massive elementary particles is an important part of contemporary physics. To create a particle of mass M requires an energy Mc2 . With enough energy, an exotic particle can be created by allowing a fast-moving proton to collide with a similar target particle. Consider a perfectly inelastic collision between two protons: an incident proton with mass kinetic energy K, and momentum magnitude p joins with an originally stationary target proton to form a single product particle of mass M. Not all the kinetic energy of the incoming proton is available to create the product particle because conservation of momentum requires that the system as a whole still must have some kinetic energy after the collision. Therefore, only a fraction of the energy of the incident particle is available to create a new particle. (a) Show that the energy available to create a product particle is given by Mc2=2mpc21+K2mpc2 This result shows that when the kinetic energy K of the incident proton is large compared with its rest energy mpc2, 2then M approaches (2mpK)1/2/c. Therefore, if the energy of the incoming proton is increased by a factor of 9, the mass you can create increases only by a factor of 3, not by a factor of 9 as would be expected. (b) This problem can be alleviated by using colliding beams as is the case in most modern accelerators. Here the total momentum of a pair of interacting particles can be zero. The center of mass can be at rest after the collision, so, in principle, all the initial kinetic energy can be used for particle creation. Show that Mc2=2mc2(1+Kmc2) where K is the kinetic energy of each of the two identical colliding particles. Here, if k mc2, we have M directly proportional to K as we would desire.
Models are particularly useful in relativity and quantum mechanics, where conditions are outside those normally encountered by humans. What is a model?
Plans for ail accelerator that produces a secondary beam of K mesons to scatter from nuclei, for the purpose of studying the strong force, call for them to have a kinetic energy of 500 MeV. (a) What would the relativistic quantity =11v2/c2be for these particles? (b) How long would their average lifetime be in the laboratory? (c) How far could they travel in this time?
Alpha decay is nuclear decay in which a helium nucleus is emitted. If the helium nucleus has a mass of 6.801027 kg and is given 5.00 MeV of kinetic energy, what is its velocity?
(a) Calculate for a proton that has a momentum of 1.00 kgm/s. (b) What is its speed? Such protons form a rare component of cosmic radiation with uncertain origins.
The planetary model of the atom pictures electrons orbiting the atomic nucleus much as planets orbit the Sun. In this model you can view hydrogen, the simplest atom, as having a single electron in a circular orbit 1.061010 m in diameter. (a) If the average speed of the electron in this orbit is known to be 2.20106 m/s, calculate the number of revolutions per second it makes about the nucleus. (b) What is the electron's average velocity?

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