Minimizing a vector in a triangle

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To determine the forces F1 and F2 for towing a truck with a resultant force of 950N along the positive x-axis, F1 is set at 20 degrees from the x-axis. The discussion centers on minimizing the angle of rope two, with one participant suggesting -90 degrees for minimal work, while the textbook indicates -70 degrees. A vector triangle approach is recommended to visualize the problem, emphasizing the relationship between the known sides and the shortest possible third side. The need for a diagram is highlighted, as it is crucial for solving the geometry involved. Understanding the angles and forces is essential for accurately calculating the required towing forces.
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Homework Statement



A truck is to be towed using two ropes. If the resultant force is to be 950N, directed along the positive x axis, determine the magnitudes of forces F1 and F2 acting on each rope and the angle at which rope two pulls to ensure that the magnitude of F2 is a minimum. F1 acts at 20 degrees from the x axis.

The Attempt at a Solution



I assumed that to minimize the work required by rope two, it would be -90degrees angle (so it is only required to pull the truck back in line). However, the book says -70degrees?
 
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Hi Shaybay92! :smile:

(have a degree: º :wink:)
Shaybay92 said:
I assumed that to minimize the work required by rope two, it would be -90degrees angle (so it is only required to pull the truck back in line). However, the book says -70degrees?

Sorry, no idea what you mean. :confused:

Anyway, just draw a vector triangle …

you know the direction and length of one side, and you know the direction of the second side …

what is the shortest the third side can be? :smile:​
 
I'm assuming based on the wording that there's a diagram that goes with this? It's kinda hard to solve a geometry problem if there's supposed to be a picture with it.
 

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