Question

Ballooning Spiders, First in Flight. 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)

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

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

Answer 1

I'm assuming that the equation they want us to use to calculate the balancing force is
\[Q=\frac{ mg }{ E_o }e^{\alpha H_{eq}}\]
But I could be wrong.
The other equation that they used seems like it's only used when the spider experiences a vertical acceleration.\[Q_{accel} = \frac{ m(a_{net}+g) }{ E_o }\] but I could be wrong.

Answer 2

I think you are right! ;/\

Answer 3

@The_Beast_Eli The only issue I'm having is that I don't know the values of a or H..

Answer 4

Equilibrium means
\[\Sigma F _{x}=0\]
so \[\Sigma F _{x}=Tsin \theta-F _{e}=0\]

Answer 5

\[\Sigma F _{y}=0\]
\[\Sigma F _{y}=Tcos \theta-mg=0\]

Answer 6

\[\Sigma F _{x}=Tsin \theta=F _{e}\]
and
\[\Sigma F _{y}=Tcos \theta=mg\]

Answer 7

Divide both
\[\frac{ Tsin \theta }{ Tcos \theta}=\frac{ F _{e} }{ mg }\]

Answer 8

\[\tan \theta=\frac{ F _{e} }{ mg }\]
m is mass in kg
g is accleration due to gravity
F is electric force

Answer 9

Its pretty simple.
Just ignore the article and information at the top.