Electrons- conservation of energy - electric potential

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An electron is projected towards a fixed proton with an initial speed of 2.4 x 10^5 m/s. The problem involves calculating the distance from the proton where the electron's speed becomes twice its initial value. The total energy of the system, comprising kinetic and potential energy, remains constant throughout the motion. Initially, at a large distance, the energy is primarily kinetic, and as the electron approaches the proton, potential energy becomes significant. The solution requires equating the total energy at the initial speed and when the speed is doubled to find the corresponding distance from the proton.
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An Electron is Projected An electron is projected with an initial speed of 2.4 x10^5 m/s directly toward a proton that is fixed in place. If the electron is initially a great distance from the proton, at what distance from the proton is the speed of the electron instantaneously equal to twice the initial value?


im having a lot of trouble with this problem i don't even know how to approach it can anyone pls help me to get started u..u
 
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The sum of the kinetic energy (1/2)mv^2 of the electron plus it's potential energy in the field of the proton k*(-e)*(e)/r is a constant (note potential energy is negative!). At large r essentially all of the energy is kinetic. Find that. Now find the energy when v is doubled. At what value of r does the total energy balance?
 

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