Block carrying a charge on a frictionless horizontal track

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SUMMARY

The discussion centers on a physics problem involving a 4.00 kg block with a charge of 50.0 µC connected to a spring with a spring constant of 100 N/m, placed on a frictionless horizontal track within an electric field of 5.00 x 10^5 V/m. The maximum expansion of the spring and the equilibrium position of the block are determined by equating the electric force to the spring's restoring force. The maximum spring expansion occurs when the electric force equals the spring force, leading to a calculated equilibrium position for the block.

PREREQUISITES
  • Understanding of Hooke's Law and spring constants
  • Knowledge of electric fields and forces
  • Familiarity with basic principles of mechanics
  • Ability to solve equations involving forces and motion
NEXT STEPS
  • Calculate the electric force acting on the block using F = Q * E
  • Apply Hooke's Law to find the maximum spring expansion
  • Determine the equilibrium position by setting electric force equal to spring force
  • Explore the effects of varying charge and spring constants on system behavior
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and electromagnetism, as well as educators seeking to enhance their understanding of force interactions in charged systems.

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Homework Statement



A 4.00 kg block carrying a charge Q=50.0 µC is connected to a spring for which k=100N/m (see diagram). The block lies on a frictionless horizontal track, and the system is immersed in a uniform electric field of magnitude E = 5.00x10^5 V/m, directed as shown. If the block is released from rest when the spring is unstretched (at x = 0), (a) by what maximum amount does the spring expand? (b) What is the equilibrium position of the block?


See attached MS Word Document for diagrams / further information. Thanks!
 

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I think at equilibrium pos, electric force is equal to restoring force. And this pos should be a max amount that spring expands because there is no other force. :-?
 

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