<p><span style=\"font-family: CMR10;\"> <p>Consider the 649 N weight held by two
ID: 1990345 • Letter: #
Question
<p><span><p>Consider the 649 N weight held by two cablesshown below. The left-hand cable had tension</p>
</span><span> T</span><span><span>2 </span></span><span>and makes an angle of Angle</span><span></span><span><span>2 </span></span><span>with the ceiling.</span></p>
<p><span>The right-hand cable had tension 530 N and makes an angle of 44 </span></p>
<p><span lang="JA"><span lang="JA"> </span></span><span>with the ceiling. </span><span>The right-hand cable makes an angle of 44</span><span>with the ceiling and has a tension of 530 N </span></p>
<p><span>a) What is the tension </span></p>
<p><span>T</span><span><span>2 </span></span><span>in the left-hand </span><span>cable slanted at an angle of Angle</span><span><span>2 </span></span><span>with respect to</span><span>the wall?</span><span>
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</span></p>
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<p>Answer in units of N</p>
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<p> </p>
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Explanation / Answer
Consider the 691 N weight held by two cables shown below. The left-hand cable had tension 840 N and makes an? angle of ? with the wall. The right-hand cable had tension 940 N and makes an angle of ?1 with the ceiling. a) What is the angle ?1 which the righthand cable makes with respect to the ceiling? Answer in units of ? .b) What is the angle ? which the left-hand cable makes with respect to the wall? This is an equilibrium problem so you must sum forces in both the x and y directions So in the x we have 840*cos(?) = 940*cos(?1) or cos(?) = 1.119*cos(?1) and in the y we have 840*sin(?) + 940*sin(?1) = 641 or sin(?) = 0.7631 - 1.119*sin(?1) Now square both eqns cos^2(?) = 1.252*cos^2(?1) and sin^2(?) = 0.5823 - 1.7078*sin(?1) + 1.252*sin^2(?1) Now add these eqns and note that sin^2 + cos^2 = 1 so 1 = 0.5823 - 1.7078*sin(?1) + 1.252 so ?1 = arcsin((1.252 + 0.5823 - 1)/1.7078) = 29.24o and from cos(?) = 1.119*cos(?1) we get ? = arccos(1.119*cos(29.24)) = 12.48o
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