Finding Minimum Force Needed to Hold Object In Place

[Oannes]

Homework Statement

A woman holds a book by placing it between her hands such that she presses at right angles to the front and back covers. The book has a mass of m = 0.75kg and the coefficient of static friction between her hand and the book is μ_s = 0.59. What is the minimum force she must apply with each of her hands F_min in Newtons, to keep the book from falling?

Homework Equations

Weight of Book = mg
Friction Force = μ_smg

The Attempt at a Solution

The weight of the book came out to be around 7.35 Newtons and the static friction force came out to be 4.34. I then divided that by 2 to get what I thought was the answer. I figured that the force that is pushing the object (7.35 Newtons) minus the force that was holding it back, friction force(4.34 Newtons) would give me the force needed to hold it without falling.

I feel that I am doing friction force incorrectly as the friction force is usually coming from the bottom of an object and the Normal Force is factored in. In this case, gravity is not playing a part on the friction force (I think) as the surfaces being affected are vertical not horizontal. Even with this assumption, I am not sure how I would go about finding the friction force of an object in this orientation. If the object was lain on an edge on the ground we could easily find the friction force against the floor, but now that it is lifted on 2 sides how would you calculate the one side? Would it perhaps be (.5g)(μ_s)(kg)?(in an ideal world). All this assuming that my original idea was correct, that I could subtract the weight of the object from the friction force to get the force needed to hold it up, then dividing by 2 to get force each hand needs to apply. Thanks in advance for any and all help.

 

[TSny]

Draw a careful free body diagram. Note that the question is asking for the force that each hand presses horizontally on the book. Although, I guess it's possible that the question is asking for the net force that each hand is exerting on the book, not just the horizontal part of that force. I think you could interpret the question either way, unfortunately.

 

[haruspex]

Friction Force = μ_smg

The static friction force has magnitude up to μ_sF_N, where F_N is the normal force. What direction is the normal force here?

 

[Oannes]

The static friction force has magnitude up to μ_sF_N, where F_N is the normal force. What direction is the normal force here?

Normal Force would be the in the horizontal direction. However, how do I get Normal force when I do not know the force of that object in the other direction? I feel as if I need some Force that the user is exerting to find it, but the force that the user needs to exert is what I'm trying to find.

 

[TSny]

Which force or forces are acting opposite to the weight in order to balance out the weight?

 

[haruspex]

Normal Force would be the in the horizontal direction. However, how do I get Normal force when I do not know the force of that object in the other direction? I feel as if I need some Force that the user is exerting to find it, but the force that the user needs to exert is what I'm trying to find.

So create a variable to represent it and write the frictional force in terms of that.
Then follow TSny's guidance in post #5.