Accelerometer via ball on string

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Discussion Overview

The discussion revolves around measuring forward acceleration using a free-swinging ball on a string. Participants explore the forces acting on the ball and seek to derive equations that relate the angle of the string to the acceleration experienced by the ball.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant inquires about the methodology for measuring forward acceleration with a free-swinging ball and requests a free body diagram or relevant equations.
  • Another participant identifies two forces acting on the ball: the downward gravitational force (mg) and the tension in the rope (T), suggesting a vectorial approach to compute the net force.
  • A participant proposes that the relationship between the angle (theta) and acceleration (a) can be expressed as tan(theta) = a/g.
  • A later reply confirms the proposed relationship, reiterating that tan(theta) = a/g, where theta is the angle the string makes with the vertical.

Areas of Agreement / Disagreement

Participants appear to agree on the relationship between the angle and acceleration as expressed by tan(theta) = a/g, but the discussion does not resolve whether this is the only or most accurate approach to the problem.

Contextual Notes

The discussion does not provide a complete derivation of the equations or a detailed free body diagram, leaving some assumptions and steps unresolved.

andrewr0x
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How would I go about measuring forward acceleration using a free-swinging ball on a stand? Could anyone post a free body diagram or an equation that might describe this?
 
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Two external forces on the ball:
downward gravitational force with magnitude (mg)
tension tangent to the the rope (T)

Compute net-force vectorially.

Use Netwon II.
Solve for the acceleration (a) as a function of angle (theta) with respect to the vertical.
 
Would tan(theta)=a/g ?
 
andrewr0x said:
Would tan(theta)=a/g ?
That's right. (Where theta is the angle the string makes with the vertical.)
 

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