Charged particle suspended from elastic cord

In summary, a charged particle with mass 200g and charge 25 µC is suspended from an elastic cord with force constant 5 N/m in an electric field of magnitude 3.7 x 10^5 N/C. The extension of the cord can be found by setting the forces in equilibrium and solving for x using the equation F_e+kx=mg.
  • #1
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Homework Statement



A charged particle with mass m = 200g and charge q = 25 µC is suspended from an elastic cord with force constant K = 5 N/m in a vertically upward electric field E of magnitude 3.7 x 10^5 N/C. What is extension of the cord when the particle is in equilibrium?

Homework Equations





The Attempt at a Solution

 
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  • #2
Hi

first draw a free body diagram. there are three forces acting on the body. [itex]mg[/itex] downwards , the force of restoration due to the elastic cord , according to Hook's law is
[itex]kx[/itex] upward and the force due to electric field [itex]F_e[/itex] upward. when in equilibrium, they balance.

[tex]F_e+kx = mg[/tex]

solve for x, the extension.
 

1. What is a charged particle suspended from an elastic cord?

A charged particle suspended from an elastic cord refers to a scenario in which a small, electrically charged object is attached to a flexible, stretchable cord or string. The cord is typically anchored at both ends, allowing the particle to hang or swing freely in response to external forces.

2. How does the elastic cord affect the motion of the charged particle?

The elastic cord acts as a restoring force on the charged particle, meaning it will pull the particle back towards its equilibrium position if it is displaced. This is due to the cord's ability to stretch and store potential energy, which is released when the cord returns to its original length.

3. What factors affect the behavior of a charged particle suspended from an elastic cord?

The behavior of a charged particle suspended from an elastic cord can be influenced by several factors, including the strength of the electric charge on the particle, the length and elasticity of the cord, and the presence of other external forces such as gravity or magnetic fields.

4. What is the significance of studying charged particles suspended from elastic cords?

Studying charged particles suspended from elastic cords can provide insights into the behavior of electrically charged particles in various environments. It can also help us understand the principles of elasticity and how it affects the motion of objects. This type of study can have applications in fields such as physics, engineering, and materials science.

5. Can charged particles suspended from elastic cords be used in practical applications?

Yes, there are practical applications for charged particles suspended from elastic cords. One example is in electrically charged dust collectors, where particles are suspended from a cord and then attracted to an opposite charge plate. Additionally, this concept is used in some types of accelerometers, which measure acceleration and motion in various devices and systems.

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