Finding Minimum Force Needed to Hold Object In Place

In summary, a woman is trying to hold a book with a mass of 0.75kg by pressing it between her hands at right angles to the front and back covers. The coefficient of static friction between her hands and the book is 0.59. To keep the book from falling, she needs to apply a minimum force of 4.34 Newtons with each hand. This can be calculated by finding the normal force and using it to determine the frictional force.
  • #1
Oannes
26
1

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 μs = 0.59. What is the minimum force she must apply with each of her hands Fmin in Newtons, to keep the book from falling?

Homework Equations


Weight of Book = mg
Friction Force = μsmg

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)(μs)(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.
 
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  • #2
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.
 
  • #3
Oannes said:
Friction Force = μsmg
The static friction force has magnitude up to μsFN, where FN is the normal force. What direction is the normal force here?
 
  • #4
haruspex said:
The static friction force has magnitude up to μsFN, where FN 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.
 
  • #5
Which force or forces are acting opposite to the weight in order to balance out the weight?
 
  • #6
Oannes said:
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.
 

What is the concept of finding the minimum force needed to hold an object in place?

The concept is based on Newton's laws of motion, specifically the third law which states that for every action, there is an equal and opposite reaction. This means that an object at rest on a surface requires a minimum force to counteract the force of gravity and remain in place.

What factors influence the minimum force needed to hold an object in place?

The factors include the weight and mass of the object, the surface it is resting on, and the force of gravity acting on the object. Friction between the object and the surface also plays a role in determining the minimum force needed.

How can the minimum force needed to hold an object in place be calculated?

The minimum force can be calculated by using the formula F=mg, where F is the force needed, m is the mass of the object, and g is the acceleration due to gravity (9.8 m/s^2). This formula takes into account the weight of the object and the force of gravity acting on it.

Can the minimum force needed to hold an object in place change?

Yes, the minimum force can change depending on the surface the object is resting on. For example, an object may require more force to hold it in place on a slippery surface compared to a rough surface with more friction.

How does understanding the minimum force needed to hold an object in place benefit us?

Understanding this concept can help us design and build structures or objects that require a certain amount of force to stay in place. It can also help us determine the stability of an object or structure and prevent it from toppling or sliding due to insufficient force.

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