Minimum horizontal force needed so book does not fall?

In summary, for part B, the normal force (N) is equal to the applied force (P) because the horizontal forces are balanced and the book is not accelerating. For part C, the minimum normal force needed to prevent the book from slipping is 378.549N, which is less than the previous maximum static friction of 131.32N. This minimum normal force can be calculated using the formula Fn=(m*g)/Us and is less than the applied force of 515N.
  • #1
Kloud
13
0

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

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  • #2
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?
 
  • #3
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?
 
  • #4
Something to make u think instead of giving the answer. Why should u compare ur answer in c with ur answer in b?
 
  • #5
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.
 
  • #6
So the for part b would the friction force be fs=m*g*us?
 
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  • #7
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?
 
  • #8
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?
 
  • #9
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.
 

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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.
 
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  • #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.
 

1. What is the minimum horizontal force needed to prevent a book from falling?

The minimum horizontal force needed to prevent a book from falling depends on the weight and size of the book, as well as the coefficient of friction between the book and the surface it is resting on. This can be calculated using the equation F = μN, where F is the minimum force, μ is the coefficient of friction, and N is the normal force.

2. How does the weight of the book affect the minimum horizontal force needed?

The weight of the book directly affects the minimum horizontal force needed to prevent it from falling. The heavier the book, the greater the minimum force required to counteract its weight and maintain its position on a surface.

3. Is the coefficient of friction the same for all surfaces?

No, the coefficient of friction varies for different surfaces. It depends on the materials and textures of the surfaces in contact. For example, the coefficient of friction between a book and a wooden table may be different than the coefficient of friction between the same book and a glass table.

4. Can the minimum horizontal force needed change over time?

Yes, the minimum horizontal force needed to prevent a book from falling can change over time due to factors such as wear and tear of the book or changes in the surface it is resting on. It is important to regularly check and adjust the force as needed to ensure the book remains stable.

5. Is it possible for a book to require more than one minimum horizontal force to prevent it from falling?

Yes, depending on the positioning of the book and the surface it is resting on, it is possible for a book to require multiple minimum horizontal forces to keep it from falling. For example, a book placed on an inclined surface may require a force to prevent it from sliding down the incline and a separate force to prevent it from tipping over.

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