Energy conservation in two dimensions

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SUMMARY

The discussion focuses on calculating the work done by a force F = −αx²i on a proton as it moves along specified paths in two-dimensional space. The force is defined with α = 14.4 N/m². The participants address three specific paths: from (0.10 m, 0) to (0.10 m, 0.5 m), from (0.09 m, 0) to (0.32 m, 0), and from (0.32 m, 0) to (0.09 m, 0). Additionally, the discussion explores whether the force is conservative and seeks to determine the potential-energy function U, defined as zero when x = 0.

PREREQUISITES
  • Understanding of line integrals in vector calculus
  • Knowledge of conservative forces and potential energy
  • Familiarity with the concept of work done by a force
  • Basic proficiency in physics, particularly mechanics
NEXT STEPS
  • Study the principles of line integrals in vector calculus
  • Learn about conservative forces and their characteristics
  • Explore the derivation of potential energy functions from force equations
  • Review examples of work done by varying forces in physics
USEFUL FOR

Students in physics, particularly those studying mechanics, as well as educators seeking to clarify concepts related to work, energy, and conservative forces.

SPiazzo
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In an experiment, one of the forces exerted on a proton is F = −αx^2i , where α = 14.4 N/m2.
(a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)?
(b) Along the straight-line path from the point (0.09 m, 0) to the point (0.32 m, 0)?
(c) Along the straight-line path from the point (0.32 m, 0) to the point (0.09 m, 0)?
If F is conservative, what is the potential-energy function for it? Let U = 0 when x = 0. (Use the following as necessary: x and α. If F is not conservative, enter NC.)

I have no idea how to do this one, there where no relevant examples in my textbook and my teacher did not teach this in our class if we have reached the topic at all.
 
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Hey SPiazzo! Can you write the Formulae for the Work done on an object By a force?
 
Work is a line integral of a force along a path. Can you calculate it?
 

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