Max Force P on a 100kg Spool w/ \mu=0.3

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In summary, the maximum force P that can be applied without causing the spool to move is 294.3 N. The book's missing term does not affect the final result but it is important to include it for accuracy.
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RedFURR
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The spool weighs 100kg, at piont A and B the [tex]\mu[/tex]=0.3
Determine the maximum force P without causing the spool to move. (see attached)
This is what I attained from Back of the Book:

[tex]\Sigma[/tex]Fx=0; 0=NA-NB(0.3)
[tex]\Sigma[/tex]Fy=0; 0=NA(0.3)+NB+P-100(9.81)
[tex]\Sigma[/tex]MO=0; 0=P(0.6)+NB(0.9)-0.3NB(0.9)-0.3NA(0.9)

Which is close to what I arrived at, but summing the moments I left out NB(0.9) which I don't understand, isn't NBs arm of action 0?
Am I wrong? if so could you explain?
or, preferably, is the book wrong?
 

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Your results are correct. The book is wrong. The missing term in the summation of moments should be NB(0.9). This is because the moment arms for both N and B are 0.9 m, so the moment on each point must be taken into account when calculating the summation of moments.
 

FAQ: Max Force P on a 100kg Spool w/ \mu=0.3

What does "Max Force P" refer to in this scenario?

"Max Force P" refers to the maximum force that can be applied to a 100kg spool while maintaining a coefficient of friction (\mu) of 0.3.

How is the maximum force calculated for this scenario?

The maximum force is calculated by multiplying the weight of the spool (100kg) by the coefficient of friction (\mu=0.3), giving a maximum force of 30 Newtons.

What is the significance of the coefficient of friction in this scenario?

The coefficient of friction represents the amount of resistance between two surfaces in contact. In this case, it determines the maximum force that can be applied before the spool begins to slide or move.

How does the weight of the spool affect the maximum force that can be applied?

The weight of the spool directly affects the maximum force that can be applied. The heavier the spool, the greater the maximum force that can be applied before it begins to slide or move.

Can the coefficient of friction be changed to increase the maximum force?

Yes, the coefficient of friction can be changed to increase the maximum force that can be applied. However, it is important to note that the coefficient of friction is dependent on the materials in contact and cannot be changed arbitrarily.

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