Electric Field Question Involving Springs and SHM

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SUMMARY

The discussion focuses on a physics problem involving a mass-spring system subjected to an electric field. The block with mass m and charge +Q is connected to a spring with spring constant k on a frictionless track. Key findings include that the maximum expansion of the spring is given by x = Eq/k, the equilibrium position is the initial position plus the spring's change in length, and the block's motion is confirmed to be simple harmonic with a period determined by the spring constant and mass. Additionally, when kinetic friction is considered, the maximum expansion adjusts to x = (Eq - μmg) / k.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with Hooke's Law and spring constants
  • Knowledge of electric forces and fields
  • Basic concepts of simple harmonic motion (SHM)
NEXT STEPS
  • Study the principles of simple harmonic motion (SHM) in detail
  • Learn about electric fields and forces, specifically in relation to charged objects
  • Explore the effects of friction on motion and equilibrium in mechanical systems
  • Investigate the mathematical modeling of mass-spring systems under external forces
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and electromagnetism, as well as educators seeking to enhance their understanding of mass-spring systems in electric fields.

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Homework Statement


A block having mass m and charge + Q is connected to a spring having constant k. The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E, directed as shown in Figure P25.11. If the block is released from rest when the spring is unstretched (at x = 0),
Image of problem here: http://www.solutioninn.com/images/P-M-E-P%20(11).PNG
(a) By what maximum amount does the spring expand?
(b) What is the equilibrium position of the block?
(c) Show that the block’s motion is simple harmonic, and determine its period.
(d) Repeat part (a) if the coefficient of kinetic friction between block and surface is μk.

Homework Equations


F(electric) = Eq
F(spring) = kx

The Attempt at a Solution


a) Drew a FBD and saw that Fs = Fe, so kx = Eq, therefore x = Eq/k
is that as far as i can go or can I solve this to find numbers?

b) the equilibrium position of the block would be the blocks initial position plus the change in x of the spring

c) i am really not sure how to solve this, if you could lead me in the right direction that would be nice

d) Fs + fk = Fe, so kx + μmg = Eq, therefore x = (Eq - μmg) / k
 
Last edited:
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does anyone have any idea on how to solve this electric force problem that involves a spring?
 

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