What is the torque on the tree from the truck?

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SUMMARY

The torque on the tree due to the tension in the rope is calculated to be 2280 Nm. The setup involves a truck creating a tension of 800N in an 8.00m rope tied to a tree trunk at a height of 3.00m, with the truck bumper positioned 0.5m above the ground. The torque is computed using the formula torque = F * r sin(theta), where the effective radius is determined to be 2.5m based on the geometry of the triangle formed by the truck, rope, and tree.

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(APPLIED TORQUE) help!

Homework Statement



ok, I've spent a good amount of time on this bastard and can't get it, help..

Man ties one end of rope 8.00m long to bumper of his truck, which is 0.5m from ground, and the other end to a vertical tree trunk at a height of 3.00m. He uses truck to create a tension of 800N in the rope...

compute magnitude of torque on the tree due to the tension in the rope, with the base of the tree acting as the reference point.



The answer is 2280 Nm

Homework Equations


torque = F * r sin(theta)


The Attempt at a Solution



I figured this is a right triangle, took the difference of the height of the bumper and the tree, pythagorean theorem to get the distance of the other side, which I used as the radius, then tried some different ways of obtaining the angle for which the rope would be pulling.
 
Last edited:
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nobody want to take a jab?
 
The perpendicular distance on the tree trunk is 2.5 meters and the hypotenuse is 8 meters - this ratio gives you the sine of the angle.
 

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