A 3.00 m long uniform strut with a mass of 15.0 kg is attached to a wall. A cable makes a...

Question:

A 3.00 m long uniform strut with a mass of 15.0 kg is attached to a wall. A cable makes a 30-degree angle with respect to the strut and holds the strut in place. A 10.0 kg light hangs from the strut at a distance of 2.00 m from the wall. (a) Find the tension in the cable, and (b) find the horizontal and vertical forces exerted by the wall on the strut.

Newton's First Law: An object remains in equilibrium if vector sum of all forces acting on object is zero.

that is {eq}\Sigma F_x=0 \ and \ \Sigma F_y =0 {/eq}

Answer and Explanation: 1

_Part(a)_

taking moment about point A we have

{eq}Tsin30 *3 = 1.5*15g +10g*2 \\ \Rightarrow Tsin30 =10g+15g \\ or T=277.7 \ N {/eq}

_Part(b)_

\SigmaF_x=0

{eq}\Rightarrow Tcos30=R_x \\ where, \ R_x {/eq}

is the horizontal component of wall's reaction

{eq}\Rightarrow R_x=277.7cos30 =240.5 \ N {/eq}

and vertical component of reaction

{eq}R_y= (10+15)g - Tsin30 = 106.15 \ N {/eq}


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Resultant Force: Definition & Formula

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Chapter 18 / Lesson 5
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In lots of situations, more than one force may act on an object. In this lesson, learn how to find the resultant force of two forces on a single object and how to use this to determine how the object will move.


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