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Homework Help: Can 3 forces of 9N, 4N, and 6N be in equilibrium?

  1. Nov 10, 2018 #1
    1. The problem statement, all variables and given/known data
    A mass of 3kg is acted upon by three forces of 4.0 N, 6.0N, and 9.0N and is in equilibrium. The 9N force is suddenly removed. Determine the acceleration of the mass.
    2. Relevant equations
    F=ma.
    3. The attempt at a solution
    My main problem with this question is that I cannot think of any situation in which these three forces would be in equilibrium. The question does not specify in which direction the forces are in or any angles (in the case of an inclined plane). How can these forces possibly be in equilibrium?
     
  2. jcsd
  3. Nov 10, 2018 #2

    berkeman

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    Welcome to the PF.

    Well, 4+6=10 > 9, so it should be possible. Just think of ways that the sum of the x-components and the sum of the y-components can both be zero. Draw a diagram and write the two equations, and see if you can solve for the relevant angles... Please show us your sketch (use the UPLOAD button) and write out your equations. Thank you. :smile:
     
  4. Nov 10, 2018 #3
    You could think of it in terms of the 4 and the 6 acting together to cancel out the 9. Is that possible?

    Suppose the 4 N and the 6 N act together in the same direction. What is their resultant force? What happens if you use that force to oppose the 9 N force?
    Suppose the 4 N and the 6 N act in directly opposite directions. What is their resultant force? What happens if you use that force to oppose the 9 N force?
    If the 4 N and 6 N are at an angle relative to each other, the situation will be in between those two situations.
     
  5. Nov 10, 2018 #4

    Charles Link

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    You can the law of cosines to compute what angle the 4N and 6N need to be relative to each other to make a resultant of 9N.
     
  6. Nov 10, 2018 #5

    Orodruin

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    Just to point out that this is not necessary to solve the problem.
    The main thing, as has been pointed out is that the forces can be in equilibrium given appropriate angles between them. What does this tell you about the resultant of the 4 N and 6 N forces?
     
  7. Nov 10, 2018 #6

    haruspex

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    Are you familiar with a "triangle of forces" in equilibrium? Can you draw a triangle with sides of those lengths?
     
  8. Nov 10, 2018 #7
    You are thinking too hard. If the system is in equilibrium, then a = 0. You also know F = 0 and F is the sum of the forces. So if you remove one force you should be able to calculate the new sum of forces and therefore the acceleration.
     
  9. Nov 10, 2018 #8

    DaveC426913

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    I've never studied forces beyond high school, so I've never encountered problems like this but, unless I miss my guess, this seems to require nothing more than basic arithmetic.
     
  10. Nov 10, 2018 #9

    Charles Link

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    I think @haruspex has the best answer for this problem in post 6.
     
  11. Nov 10, 2018 #10

    haruspex

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    That is the neatest way to solve the given problem, yes, but the OP's question in the forum is a little different.
     
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