Minimum horizontal force needed so book does not fall?

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Homework Help Overview

The discussion revolves around determining the minimum horizontal force required to prevent a book from slipping, with specific values provided for normal force, static friction, and mass. The subject area includes concepts of static friction, forces, and Newton's laws of motion.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants explore the relationship between static friction and normal force, questioning whether the static friction force must be at its maximum value. There are attempts to clarify the calculations for different parts of the problem and to understand the implications of the forces acting on the book.

Discussion Status

The discussion is active, with participants providing guidance and prompting each other to reconsider their assumptions and calculations. There is an exploration of how to relate the forces in different parts of the problem, and some participants express confusion about the application of formulas and the conditions under which they apply.

Contextual Notes

Participants note that the problem does not specify whether the static friction is at its maximum and discuss the implications of this uncertainty on their calculations. There is also mention of a free body diagram that may aid in understanding the forces involved.

Kloud
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Homework Statement


Part C of problem Please see attachment : What is the minimum horizontal force needed to keep the book from slipping. Note that P=515N, and P=normal force, Fs=131.32N, Us=.255, M=9.85kg

Homework Equations


Fn=(m*g)/Us

The Attempt at a Solution


My answer is 378.549N, which makes no sense becasue in the previous part my force of static friction was 131.32N. PLease help!
 

Attachments

  • Screen Shot 2016-06-08 at 8.17.39 PM.png
    Screen Shot 2016-06-08 at 8.17.39 PM.png
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Hello and Welcome to PF!

Your answer to b is incorrect. Keep in mind that the formula ##f_s^{\rm {max}} = \mu_s N## is a formula for the maximum possible static friction force for the two surfaces. Is the static friction force in part b necessarily equal to the maximum possible static friction force?
 
Yes it is. Thats why I used the max formula. Part C on the other hand I am not sure about? What do you think about my answer for it?
 
Something to make u think instead of giving the answer. Why should u compare ur answer in c with ur answer in b?
 
Kloud said:
Yes it is. Thats why I used the max formula.
Why do you say that the friction force must be at its maximum value in part (b)? When ##f_s## is at its maximum value, the object is on the verge of slipping. But there is nothing in the statement of problem that says the object is on the verge of slipping in part (b).

You should be able to deduce the value of the friction force in part (b) without using ##f_s^{\rm {max}} = \mu_s N##.
Set up ΣFy = may.
 
So the for part b would the friction force be fs=m*g*us?
 
Last edited:
U r getting confused. All your calculations are correct. U just have to understand them fundamentally. Think about whether the answer in c should be compared with b or with a?
 
Ye your right, I am confused. I am pretty sure part b is correct cause the only equation I have for static friction is the max formula, while for part C I am kinda sure its correct cause initially we apply 515N to the book, so if I am getting 378.54, that's less force so I assume it to be the mininmum Normal force. Also I am not sure how to derive
the Friction force from Fy = may?
 
The frictional force will balance the weight of the book F equals mg
 
  • #10
Kloud, it might help to go back to part (a). How did you determine the value of the normal force?
 
  • #11
Fn=P cause both forces is horizontal.
@Parixit, so are you saying for part B, Fs=(9.8m/s^2)*(9.85kg), not Fs=Us*N? Cause the problem does not specify max static friction or not.

I am confused now. How did we go from Fy=may to Fy=mg?, I know g is the gravitational acceleration, but if you change a to g wouldn't it be Fy=-mg?
 
  • #12
Kloud said:
Fn=P cause both forces is horizontal.
Just because two forces are horizontal doesn't mean that they have to be equal. Try to give a logical argument based on principles of physics. I have attached a free body diagram below. See if you can use Newton's second law ΣFx = max to deduce that Fn = P.
 

Attachments

  • FBD.png
    FBD.png
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  • #13
Kloud said:
Fn=P cause both forces is horizontal.
@Parixit, so are you saying for part B, Fs=(9.8m/s^2)*(9.85kg), not Fs=Us*N? Cause the problem does not specify max static friction or not.

I am confused now. How did we go from Fy=may to Fy=mg?, I know g is the gravitational acceleration, but if you change a to g wouldn't it be Fy=-mg?
No, I thought u were talking about frictional force in part c. For part b frictional force would be Us * N. And since the book is not moving horizontally, it means the horizontal forces are balanced. So N equals P.

Also there is no need of considering max static friction in this problem. Hope that clarifies.
 
Last edited:
  • #14
I agree with your answer for the normal force (515N). The book isn't accelerating horizontally so the horizontal forces must sum to zero.

For question b apply the same reasoning. First you check that the MAX friction force (131N) is greater than the force due to gravity (approx 98N). That shows the book isn't sliding. If it's not sliding then it's not accelerating so the vertical forces must sum to zero. The actual friction force is NOT 131N.

For question c...You know the minimum friction force required to stop the book sliding and the coefficient of friction so you can calculate the minimum normal and minimum applied force required.
 

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