Question

A man ties one end of a strong rope 9.00 m long to the bumper of his truck, 0.588 m from the ground, and the other end to a vertical tree trunk at a height of 3.81 m. He uses the truck to create a tension of 7.71 102 N in the rope. Compute the magnitude of the torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point.

Answer 1

Answer:2.742 kN-m

Explanation:

Given

Height at which rope is tied to the tree$h_1=3.81 m$

height at which rope is tied to the bumper is $h_2=0.588 m$

Tension in the rope$=7.71\times 10^2 N$

$T\cos \theta$ will provide torque to tree w.r.t to ground

$\sin \theta =\frac{3.81-0.588}{9}=0.358$

$\theta =20.97^{\circ}$

Torque$=T\cos \theta \times 3.81$

Torque$=771\cos (20.97)\times 3.81=2.742 KN-m$