In Problems 74 through 76 you are given the equation(s) used to solve a problem. For each of these,
a. Write a realistic problem for which this is the correct equation(s).
b. Finish the solution of the problem.
a. "Find the speed of a proton launched from a distance of to a charge of with a speed of while at a distance of from the charge."
Given equation :
Theory used :
Coulomb's law states that the electrical force between two charged objects is directly proportional to the product of the quantity of charge on the objects and inversely proportional to the square of the separation distance between the two objects.
a. Real life problem :
"Find the speed of a proton launched from a distance of to a charge of with a speed of while at a distance of from the charge."
b. We can derive the following numerical equality from the law of conservation of energy, which is presented in the exercise:
We can simplify this by conducting calculations, as shown below, to make it easier:
Now we can calculate the speed :
In the form of radioactive decay known as alpha decay, an unstable nucleus emits a helium-atom nucleus, which is called an alpha particle. An alpha particle contains two protons and two neutrons, thus having mass and charge . Suppose a uranium nucleus with protons decays into thorium, with protons, and an alpha particle. The alpha particle is initially at rest at the surface of the thorium nucleus, which is in diameter. What is the speed of the alpha particle when it is detected in the laboratory? Assume the thorium nucleus remains at rest
Physicists often use a different unit of energy, the electron volt, when dealing with energies at the atomic level. One electron volt, abbreviated eV, is defined as the amount of kinetic energy gained by an electron upon accelerating through a 1.0 V potential difference. a. What is 1 electron volt in joules? b. What is the speed of a proton with 5000 eV of kinetic energy?
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