Calculating Electrostatic Force on a Suspended Gossamer Spider

In summary: I think the angle is just messed up, it should be an angle relative to the vertical direction. I went ahead and solved for the missing force, and it came out to be 5.5 x 10-4N.
  • #1
Callix
106
0

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)eaHeq
(3). Qaccel = [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

Phy2.png

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! :)
 
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  • #2
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?
 
  • #3
That angle does not make sense if it is a pendulum problem?
 
  • #4
Ah right, the direction ("E of N") is weird. It should be an angle relative to the vertical direction.
 
  • #5
Do you maybe know how do the Earth's electrostatic field come about? 5 kV!
 
  • Like
Likes Callix
  • #6
See the references 11 and 12 in the paper linked in post 1.
The voltage depends on the distance you consider.
 
  • #7
I realized that it is just a statics problem. Break the forces into x and y components and solve for the missing Fe . 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? :)
 
  • #8
mfb said:
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.
 

1. What is an electrostatic problem?

An electrostatic problem is a problem that involves the study of stationary electric charges and their interactions with other charges and electric fields. It is a branch of physics that deals with the behavior of electrically charged particles and the forces between them.

2. What are some common examples of electrostatic problems?

Some common examples of electrostatic problems include charging by friction, the attraction or repulsion of charged objects, and the behavior of electric fields around charged objects.

3. How are electrostatic problems solved?

Electrostatic problems are typically solved using mathematical equations, such as Coulomb's law, which describes the force between two charged particles. These equations can then be used to calculate the electric field, potential, and other properties of the system.

4. What are some applications of electrostatics?

Electrostatics has many practical applications, such as in the design of electronic devices, electrostatic precipitators for air pollution control, and inkjet printers. It is also used in the study of lightning, plasma physics, and the behavior of materials in high-voltage environments.

5. What are some challenges in solving electrostatic problems?

One of the main challenges in solving electrostatic problems is the complex nature of electric fields and their interactions with charged particles. Additionally, the behavior of electrostatic systems can be affected by factors such as the shape and size of objects, and the presence of other electrically charged objects in the vicinity.

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