Torques in equilibrium w/ angle

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SUMMARY

The discussion focuses on calculating the force required to balance a meter stick at an angle of 30 degrees with respect to the vertical, with the pivot point located at 1/4 of its length. The equilibrium condition is established using the torque equation, where the sum of torques (sigma T) equals zero. The gravitational torque (T1) is zero at the pivot, while the tension in the string (T2) is expressed as rFsin(theta). Key considerations include the center of mass and the correct application of sine and cosine functions in torque calculations.

PREREQUISITES
  • Understanding of torque and equilibrium principles
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Familiarity with the concept of center of mass
  • Basic mechanics involving forces and lever arms
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supercherrie
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on a meter stick the pivot point is placed at 1/4 its length; predict the force needed to balance the meter stick by pulling upward on the end of it with a string making an angle of 30 degrees w/ respect to the vertical.

Me trying to solve it:
sigma T=0
T1+T2=0
T1 = 0 <--this is the pivot point, i think it equals 0 b/c we what to reach equilibrium
T2 = rFsin(theta)
0+rFsin(theta)
F=-0/(rsin(theta)) ?
 
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supercherrie said:
T1+T2=0
T1 = 0 <--this is the pivot point, i think it equals 0 b/c we what to reach equilibrium
It's the '=0' in 'T1+T2=0' that says we're to reach equilibrium. T1 is the torque from the gravitational force. Where is the centre of mass of the stick? How far from the pivot point? What torque does it exert?
As for the string, it's 30 degrees to the vertical. Be careful about sine versus cosine. (As a check, I always think to myself, what if the specified angle were zero? Would the force be zero or max?)
 

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