Potential and Differential equations

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SUMMARY

The discussion focuses on a particle of mass 3 kg moving in the xy-plane under a force field defined by the potential φ = 12x(3y - 4x). The task involves setting up and solving differential equations to describe the particle's motion, including finding its position and velocity over time. Key equations include Newton's second law, which relates force to acceleration, and the relationship between acceleration a(t) and position r(t). The discussion highlights the need for a clear understanding of these concepts to solve the posed problems effectively.

PREREQUISITES
  • Understanding of Newton's Second Law
  • Familiarity with differential equations
  • Knowledge of potential energy in force fields
  • Basic concepts of motion in two dimensions
NEXT STEPS
  • Study the derivation of force from potential energy functions
  • Learn to set up and solve second-order differential equations
  • Explore the relationship between acceleration, velocity, and position in physics
  • Investigate numerical methods for solving differential equations
USEFUL FOR

Students and professionals in physics, particularly those focusing on classical mechanics, as well as anyone involved in solving differential equations related to motion in force fields.

abramsay
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Homework Statement


A particle of mass m = 3kg moves in the xy plane under the influence of a force field having potential φ = 12x(3y - 4x)
The particle starts at a point with position vector r = 10i - 10j.
a) set up the differential equations and conditions describing the motion.
b) solve th differential equations set up.
c) Find the position at any time.
d) Find the velocity at any time


Homework Equations





The Attempt at a Solution


Really I can't do (a) and (b) but I know I would need it to solve (c) and (d)
 
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abramsay said:

The Attempt at a Solution


Really I can't do (a) and (b) but I know I would need it to solve (c) and (d)

What force does the given potential exert on the particle? What does Newton's 2nd law tell you about the effect of that force on the particle? How is acceleration [itex]\textbf{a}(t)[/itex] related to position [itex]\textbf{r}(t)[/itex]?
 

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