Question

During a storm, a tree limb breaks off and comes to rest across a barbed wire fence at a point that is not in the middle between two fence posts. The limb exerts a downward force of 136 N on the wire. The left section of the wire makes an angle of 10° relative to the horizontal and sustains a tension of 447 N. Find the magnitude and direction of the tension that the right section of the wire sustains.

magnitude N

direction ° (counterclockwise from x-axis)

Answer 1

here,

force exerted by the limb , F = 136 N

T1 = 447 N

theta1 = 10 degree

let the tension in the left wire be T2 and the angle with horizontal be theta2

T1 * cos(theta1) - T2 * cos(theta2) = 0

447 * cos(10) - T2 * cos(theta2) = 0 .....(1)

and

T1 * sin(theta1) + T2 * sin(theta2) - F = 0

447 * sin(10) + T2 * sin(theta2) - 136 = 0 .....(2)

from (1) and (2)

T2 = 533.34 N

theta2 = 34.37 degree

the tension in the right wire is 533.34 N 34.37 degree counterclockwise from +x axis