What additional force is needed to keep the object at rest?

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Homework Help Overview

This problem involves vector forces in a calculus context, specifically determining the additional force required to maintain an object at rest under the influence of two given forces.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need to find a third force that, when combined with the two given forces, results in a net force of zero. There is uncertainty about the initial steps and the correct interpretation of the problem.

Discussion Status

Some participants are exploring the relationship between the forces and attempting to set up equations based on the requirement for equilibrium. There is an indication of potential calculation errors, and guidance is being offered to clarify the approach.

Contextual Notes

There is a mention of working in either two or three dimensions, which may affect the interpretation of the forces involved. The original poster expresses confusion about the relevance of their initial calculations.

ArcadeEdge
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This is a problem from my Calculus class in the sections about vectors.

Homework Statement


Two forces F1 = 2i + 6j and F2 = 2i -2j act on an object. What additional force is needed to keep the object at rest?


Homework Equations


I'm not sure where to start.


The Attempt at a Solution


I know for the body to be at rest it has to equal 0.
I've tried finding the displacement between the two given vectors which gives me <0, 81>. I'm not sure if that is even relevant. The only thing I really get right now is that something has to equal zero. I feel like this is an easy problem but I don't know where to get started..

thanks in advance.
 
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So we're looking for the third force F3, correct? Let's write it out as F3 = x i + y j + z k where x, y and z are unknown at this moment. (I'm assuming you're working in three dimensions, if you're only working in two, forget the "z k" term)

Now think about what the 'only thing you really get right now' tells you about the relation between these three forces...
 
You add them together and set them equal to zero and solve for xi and yj right? When I do that I get 0 for both x and y.
 
The technique sounds right, I'm guessing you're making a math mistake

can you type it out?
 

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