Chandelier horizontal force help

AI Thread Summary
To displace a 26.5 kg chandelier hanging from a 4.11 m wire by 0.100 m, a horizontal force must be calculated based on static equilibrium principles. The tension in the wire is determined to be 260 N. In static equilibrium, the net force in any direction is zero, requiring the horizontal force to balance the horizontal component of the tension. The analysis involves resolving forces into their components, particularly focusing on the angle between the tension and the horizontal. Understanding these principles is crucial for accurately determining the necessary horizontal force for displacement.
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A 26.5 kg chandelier hangs from a ceiling on a vertical 4.11 m long wire. What horizontal force would be necessary to displace its position 0.100 m to one side?
I know that the tension on the wire would be 260 N but I still can't figure out the force need to displace it .100
 
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Static equilibrium : Could you proceed with this?
 

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I tried but I'm still just as stuck as before.
 
Because the object is in static equilibrium, the net force acting on it in any direction will be zero. Let's take the horizontal x-component. Left direction: Negative. Right direction positive.
<br /> \begin{multline*}<br /> \begin{split}<br /> &amp;Newton\ 2nd\ Law:\\<br /> &amp;\sum\vec{F}=m\vec{a}\\<br /> &amp;F+(-Tcos\ \theta) = 0\\<br /> &amp;Vertical\ y\ component:\\<br /> &amp;Upward\ direction:\ positive;\ Downward:\ Negative\\<br /> &amp;Tsin\ \theta+(-mg)=0\\<br /> &amp;\theta\ is\ the\ acute\ angle\ between\ T\ and\ the\ horizontal.\\<br /> \end{split}<br /> \end{multline*}<br />
 

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