Nonuniform Acceleration - Radio Waves Effect on Ionosphere Electron

[Inklings]

Hi,

Reading through an Introductory Mechanics Textbook, I don't understand a part of an example on Nonuniform Acceleration - The effect of a Radio Wave on an Ionosphere Electron.

I've attached the link.

Can someone please explain how:

a₀ = (-eE₀/m)sinωt

By my reasoning,

since at t=0, sinωt = sin0 = 0
∴ a₀ = 0

Thanks heaps in advance,
Sofia :)

 

[berkeman]

I don't see the link. Maybe try again?

 

[cepheid]

Welcome to PF Inklings (or Sofia, actually!),

There is no link attached. I will make some assumptions about what is going on in your example. If the electric field is given by the function:

E(t) = E₀sinωt

Then, the acceleration is F/m = (qE)/m, where q is the charge that the field is acting on. In the case of an electron, q = -e, and we have for the acceleration as a function of time:

a(t) = -eE/m = (-eE₀/m)sinωt

Now, we know that under a sinusoidal force, the acceleration will be sinusoidal as well, so we can write it in the general form a(t) = a₀sinωt where a₀ is the amplitude. *By comparison* with the expression for a(t) above, we conclude that a₀ = (-eE₀/m).

This makes sense. The amplitude (max value in either direction) of the acceleration is just the amplitude (max value) of the force, divided by the mass.

The problem in your original post was that you mistakenly had the factor of sinωt in your expression for a₀.