What Is the Plane's Acceleration Based on Pendulum Shift?

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SUMMARY

The discussion focuses on calculating the acceleration of a jet plane based on the shift of a pendulum during uniform acceleration. Given a pendulum length of L = 1.04 m and a mass of m = 0.43 kg, the equilibrium position shifts to D = 0.380 m. Participants emphasize the importance of identifying all forces acting on the pendulum and applying Newton's second law (F=ma) to both vertical and horizontal components to derive the plane's acceleration. The solution involves analyzing the free body diagram and understanding the dynamics of the pendulum in an accelerating frame.

PREREQUISITES
  • Understanding of Newton's laws of motion, specifically F=ma.
  • Knowledge of pendulum dynamics and equilibrium positions.
  • Ability to draw and interpret free body diagrams.
  • Familiarity with basic trigonometry for resolving forces.
NEXT STEPS
  • Study the application of Newton's second law in non-inertial reference frames.
  • Learn how to calculate pendulum motion under acceleration.
  • Explore the concepts of tension and gravitational forces in pendulum systems.
  • Investigate the effects of acceleration on equilibrium positions in dynamic systems.
USEFUL FOR

Students in physics, particularly those studying mechanics, as well as educators and anyone interested in understanding the dynamics of pendulums in accelerating frames.

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Homework Statement


A pendulum has a length L = 1.04 m, with mass m=0.43 kg at the end. It hangs straight down in a jet plane about to take off as shown by the dotted line in the figure. The jet then accelerates uniformly, and while the plane is accelerating, the equilibrium position of the pendulum shifts to the position shown by the solid line, with D = 0.380 m. Calculate the magnitude of the plane's acceleration.
physics.gif


Homework Equations



F=ma

The Attempt at a Solution



I really don't know where to start with this problem.. I drew a free body diagram for the pendulum weight and didnt know what to do next


Thanks for anyone who can help :)
 
Physics news on Phys.org
First identify all the forces acting on the mass. (If you've drawn your free body diagram, you've got that step done.) Now apply Newton's 2nd law to both vertical and horizontal components.
 

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