Simple Physics Problem?

Here is a problem I encountered and have had a little trouble with. I'm not quite sure how to place the signs when I make the equation to solve this problem

Update:

I'm pretty sure the equation is:

M1g - f = - k*x - B*x' - Mx" 

which gives the result f = 29.33

Can anyone verify?

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2 Answers

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  • 1 month ago

    You have failed to give any description so I am considering a mass is a) below its rest position and the spring provides an upward force.  b) moving downwards so a viscous damper is providing an upwards force.  c) is accelerating downwards.

    Your signs are terribly confusing as written.

    Remember the principle is that F = ma so you need to get all the forces on one side using the correct signs, then the resulting acceleration on the other.

     M1 g is also a force but acts downwards ( positive) .

     F + M1 g - k x - B x'  Note that if we take x as "down = positive" then a positive value of force would be down and a negative value would be up.

    Using F = ma then this force gives rise to an acceleration.

    m x''  = ma = F + M1 g - k x - B x'

    -> F = mx'' - m1g + kx + bx' = 7*8 -7*9.81 -9*8 - 3*2 = -90.67 ie an upwards force.  Now your equation is wrong.  If x'' = g then

    m1g = m x'' But you have effectively m1g = -mx'' so you know that there is an error here.

    Hence using the principle of F=ma gives a clearer and less error prone picture.

    Given that we disagree it must be in the interpretation of the values.

    And THAT is what is missing in the question.

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  • 1 month ago

    I’ll assume the absence of any units is not a mistake (or you’ll lose a lot of marks)!

    The blue symbol on the right suggests we take are meant to take downwards as positive, with the equilibrium position as x=0.

    Weight acts down: this force is +Mg (not sure where you got M1g from) where g is a positive value.

    Force ‘f’ is shown acting upwards, which means it is not clear what sign is required for the answe (final value of f).  So let’s work out its magnitude, |f|.  So this force acting on M is -|f|.

    For a small downwards (x is positive) displacement, the spring gets compressed so exerts an upwards (-) force.

    For a small upwards (x is negative) displacement, the spring gets stretched so exerts and downwards (+) force.

    So spring's force on M is  -kx (minus sign ensures force’s direction is correct depending if x is positive or negative).

    For velocity, ẋ the damping force acts in the opposite direction to ẋ so damping fore is -Bẋ.

    Resultant force, F, is sum of above forces:

    F = Mg - |f| - kx – Bẋ

    Using F = ma gives:

    Mg - |f| - kx – Bẋ = Mẍ

    |f| = Mg - kx – Bẋ – Mẍ

    Put the given values in:

    |f| = 7*9.81 - 9*8 - 3*2 – 7*8

    . . = -65.33 which should be rounded to say -65

    A magnitude can’t be negative so this could mean:

    - the diagram is wrong and f is acting *down*;

    - there is a mistake in the question (e.g. minus sign missing from a value);

    - I’ve made a mistake!

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