Calculating Electrostatic Force on a Suspended Gossamer Spider

[Callix]

Homework Statement

You are studying Gossamer Spiders in a biology research lab and marvel at their ballooning stunts. These Spiders disperse by spinning strands of silk in open air. The flight of these spiders is electrostatic in nature because everything that moves through air develops static charge and because the glue that coats a spider web strand has electrostatic properties that causes the web to latch onto all charged particles, from pollen to flying insects.2 Suppose a Gossamer Spider has a mass of 5.5 x 10-4kg. If the spider is suspended from a tree branch by a 1.4-m strand of silk, suspended by an angle of 22.00° E of N, what amount of electrostatic force is necessary to keep the spider in equilibrium? Assume the electrostatic force is entirely horizontal. (See reference below)

http://arxiv.org/pdf/1309.4731v1.pdf

Homework Equations

(1). E(h) = E₀*e^-ah Vm^-1
(2). Q = (mg/E₀)e^aH_eq
(3). Q_accel = [m(anet+g)]/E₀
(4). F = qE

The Attempt at a Solution

Knowns:
mass = 5.5 x 10^-4
length of the strand of silk = 1.4m
angle = 22deg E of N

This is the diagram given to us.

My initial attempt was to take equation (2). and substitute it into the equation F=qE. However, I ran into another a small situation. I wasn't sure if it was safe to cancel out the E from F=qE and the E₀ from Eq (2). I didn't want to make assumptions, but my thought was that both are referring to the same electric field. My second issue is that I don't know the value of a or h.

Consequently, I moved to a different idea and started to use Eq (3) and plugged it into F = qE. However, then I began to see that the article states that this is equation is used for when the spider experiences an initial acceleration. Besides the gravitational constant (g), I don't have any other acceleration mentioned in problem description.Any help would be greatly appreciated! :)

 

[mfb]

Where do equations 1 and 2 come from and what do they mean? What are the variables used there?

The spider on its string is a pendulum. What do you know about forces at a pendulum?

 

[andrevdh]

That angle does not make sense if it is a pendulum problem?

 

[mfb]

Ah right, the direction ("E of N") is weird. It should be an angle relative to the vertical direction.

 

[andrevdh]

Do you maybe know how do the Earth's electrostatic field come about? 5 kV!

 

[mfb]

See the references 11 and 12 in the paper linked in post 1.
The voltage depends on the distance you consider.

 

[Callix]

I realized that it is just a statics problem. Break the forces into x and y components and solve for the missing F_e . Sorry I never updated the thread! I had to take a break from the problem and when I went back to it I had come to the realization that the article is pretty useless when solving this problem. Don't you love professors? :)

 

[Callix]

Ah right, the direction ("E of N") is weird. It should be an angle relative to the vertical direction.

The direction given to us in the initial problem was weird... but the diagram is the one that our professor drew for us for clarification.