Show that Newton's 2nd Law is *Not* valid in a reference frame

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SUMMARY

The discussion centers on demonstrating that Newton's Second Law, expressed as F = ma, is not valid in a non-inertial reference frame undergoing constant acceleration. Participants analyze the transformation of variables between the laboratory frame and the moving frame, emphasizing that while Newton's Second Law holds in inertial frames, it fails in non-inertial frames due to the introduction of fictitious forces. The key equations discussed include the transformation of position and acceleration, dx^1/dt = dx/dt - v, and the implications of constant velocity on force and acceleration relationships.

PREREQUISITES
  • Understanding of Newton's Laws of Motion
  • Familiarity with inertial and non-inertial reference frames
  • Basic knowledge of calculus, particularly derivatives
  • Concept of fictitious forces in physics
NEXT STEPS
  • Study the implications of non-inertial reference frames in classical mechanics
  • Explore the concept of fictitious forces and their effects on motion
  • Learn about the Lorentz transformations in special relativity
  • Investigate advanced applications of Newton's Laws in varying reference frames
USEFUL FOR

Physics students, educators, and anyone interested in the foundational principles of mechanics and the limitations of classical physics in non-inertial frames.

Tonia
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Homework Statement


Show that Newton's Second Law is NOT valid in a reference frame moving past the laboratory frame of problem 1 with a constant acceleration?
Problem 1: In a laboratory frame of reference, an observer notes that Newton's Second Law is valid. Show that it is also valid for an observer moving at a constant speed, small compared with the speed of light, relative to the laboratory frame.
dx^1/dt = dx/dt-v
d^2x^1/dt^2= d^2x/dt^2
force new = force old
acceleration = d^2x/dt^2 and if v is constant = dv/dt = 0

Homework Equations


F = ma

The Attempt at a Solution


I am not sure how to solve it
 
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You don't have to be sure of the approach to use the approach.
Try showing that the force on the object is not equal to it's mass multiplied by it's acceleration.
 

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