What is the torque on the tree from the truck?

AI Thread Summary
The discussion focuses on calculating the torque exerted on a tree by a rope tied to a truck, with the rope creating a tension of 800N. The setup involves a right triangle formed by the height difference between the truck bumper and the tree trunk, with the rope length being 8.00m. The participant attempts to find the torque using the formula torque = F * r sin(theta), identifying the perpendicular distance from the base of the tree to the line of action of the force as 2.5 meters. After calculations, the correct torque value is determined to be 2280 Nm. The conversation highlights the challenges in visualizing the geometry and applying trigonometric principles to solve the problem.
throwerx
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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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