Solving 3 Variables with 2 Equations: Min Force Needed

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Discussion Overview

The discussion revolves around a physics problem involving three variables and two equations related to forces acting on a block, specifically focusing on the minimum force needed to initiate movement. The scope includes conceptual reasoning about tension, normal force, and friction in both vertical and horizontal movements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant notes the challenge of solving for three variables with only two equations, particularly questioning the relationship between normal force and tension when both are acting on the block.
  • Another participant suggests that the block will only start to move when the tension's vertical component equals the block's weight, raising the need to consider both vertical and horizontal components of tension.
  • A participant expresses concern about determining tension if the initial movement is horizontal, reiterating the issue of having three variables and two equations.
  • Further clarification is provided regarding the conditions under which the block would move horizontally, emphasizing the role of static friction and the need for the horizontal component of tension to exceed the frictional force.
  • One participant mentions that the coefficient of friction (mu) is given as 0.3, indicating a potential path to solving the problem but remains uncertain about the overall approach.

Areas of Agreement / Disagreement

Participants express varying views on how to approach the problem, particularly regarding the conditions for vertical versus horizontal movement and the implications for the number of equations needed. No consensus is reached on a definitive method to solve the problem.

Contextual Notes

The discussion highlights limitations related to the assumptions about the initial movement direction and the dependence on the coefficient of friction provided. The relationship between the forces involved remains unresolved.

Who May Find This Useful

Readers interested in mechanics, force analysis, and problem-solving in physics may find this discussion relevant, particularly those grappling with similar problems involving multiple forces and variables.

trajan22
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The problem I am having is that in all the figures (in the image) I have 3 variables with only 2 equations. In figure 3 The only way I could solve for the variables would be to set the normal force equal to the weight, however if the tension is also pulling up it would decrease the normal force. What am I missing?

Any help would be greatly appreciated.

http://thumb9.webshots.net/t/62/462/7/59/6/2342759060052201329kWwXpL_th.jpg
 
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The sketches are a little hard to decipher. But if I understand them correctly, the block will start to move only when the tension is enough to counteract the weight of the block. Which means that the tension in the rope attached to the block will have to have a vertical component equal to the weight of the block (and a horizontal component of ?). That's if the initial motion of the block is vertical. Seems like you also need to check to see if slightly less tension would lighten the block enough so that the horizontal component of the tension could slide the block sideways...
 
That makes sense if the initial movement is vertical. But how could I find the tension if the initial movement is horizontal. Would'nt that bring us back to the 3 variable 2 equation thing?

If it would help I could scan the problem from the book also.
 
trajan22 said:
That makes sense if the initial movement is vertical. But how could I find the tension if the initial movement is horizontal. Would'nt that bring us back to the 3 variable 2 equation thing?

If it would help I could scan the problem from the book also.

I'm not sure about the number of equations thing, but the first movement will be horizontal if the horizontal component of the tension required to overcome the diminishing horizontal static friction force (F=mu*N) becomes big enough to slide the block, before the vertical component is enough to lift the block. Are you given the mu for the block on the surface? If not, then they must just be asking for the lifting event.

And if it's the lifting event, then yes, the vertical component of the tension would equal the weight of the block. Does that give you an equal number of unknowns and equations now? (I don't know -- I haven't looked in detail at the problem)
 
Last edited:
They do give mu as .3. I think I might be able to solve the problem now. If I can't Ill post back. thanks for the help.
 

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