Interactive Learningware 4.3 provides a review of the concepts thst re i point t

Question

Interactive Learningware 4.3 provides a review of the concepts thst re i point that is not in the middle between two fence posts. The limb exerts a ve to the horizontal and sustans a tension of 447 N. Find the magnit During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a downward force of 154 N on the wire. The left section of the wire makes an angle of 13 relat and direction of the tension that the right section of the wire sustains magnitude directionL "(counter clockwise from x-axis) Additional Materials Section 4.11

Explanation / Answer

To solve this problem, first off all break the forces in X and Y components and then balance them.

For X - direction, we have -  

-447N*cos(13) + T2*cos(2) = 0

=> T2*cos(2) = 435.5---------------------------------------------------(i)

For Y - direction -

447*sin(13) + T2*sin(2) - 154 = 0
=> T2*sin(2) = 154 - 447*sin(13) = 53.4--------------------------------(ii)

By doing (ii) / (i) -

sin(2)/cos(2) = 53.4 / 435.5 = 0.123

=> tan(2) = 0.123

=> 2 = arctan(0.123) = 6.99 deg

and T2 = 435.5 / cos(6.99) = 438.8 N

so, the magnitude = 438.8 N

Direction = 6.99 deg

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