Finding spring constant with electron on end

[briteliner]

Homework Statement

Calculate the spring constant of a spring with an electron mass at itsend and the frequency 4.9X10^14 Hz. mass of electron: 9.11X10^-31 g

Homework Equations

F=kx
k=mg/x

The Attempt at a Solution

Since i know the frequency, i can get the period, but where i am stuck is how to turn the period into an x value that i can use to determine the value of k. should i be using coulomb's law for this?

 

[Defennder]

It's funny how they used an electron instead of any mass, but since there's no consideration of any electrostatic forces, you can just ignore the electron charge. Just plug in the SHM formula for period/frequency with the given info to find the spring constant.

 

[baba89]

I would approach this problem by first understanding the concept of a spring constant. The spring constant, denoted as k, is a measure of the stiffness of a spring and is defined as the force required to stretch or compress a spring by a certain distance. In this case, we have an electron with a mass of 9.11X10^-31 g attached to the end of the spring.

To determine the spring constant, we need to use the equation F=kx, where F is the force applied to the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position. In this problem, we are given the frequency of the spring, which can be used to calculate the period (T) of the oscillation using the formula T=1/f, where f is the frequency.

Now, we can use the equation for the period of a simple harmonic oscillator, T=2π√(m/k), where m is the mass of the object attached to the spring. In this case, m is the mass of the electron, 9.11X10^-31 g. Rearranging this equation, we get k=m(4π^2/T^2).

Substituting the values given in the problem, we get k=(9.11X10^-31 g)(4π^2)/(1/4.9X10^14 Hz)^2= 1.18X10^-28 N/m. This is the spring constant of the spring with an electron mass at its end and a frequency of 4.9X10^14 Hz.

It is important to note that Coulomb's law, which describes the force between two charged particles, is not applicable in this scenario as there is no mention of any other charged particle interacting with the electron-spring system. The equation F=kx, derived from Hooke's law, is the appropriate equation to use in this situation.

In conclusion, by understanding the concept of spring constant and using the given information, we can calculate the spring constant of a spring with an electron mass at its end and a frequency of 4.9X10^14 Hz. This value can be used to further study the behavior of the spring and its oscillations.