A book rests at an angle against one side of a bookshelf...

Looking at your equations, I see that the force of 1.52 is used in one place, while the force of 1.69 is used in another. That is a dead giveaway that you are working on different problems. I can't say for sure without seeing the original problem, but I'll bet you have two different masses and two different angles here. It is possible, of course, that I am wrong. You might have just made a careless mistake in copying the equations. So check your work carefully. If you still can't find the problem, post the original question.In summary, the conversation is discussing the process of finding Fb using trigonometric functions and equations involving different masses
  • #1
madge
1
0
Homework Statement
A 0.135 kg
book rests at an angle against one side of a bookshelf. The magnitude and direction of the total force exerted on the book by the left side of the bookshelf are given by

|𝐹L|=0.575 N𝜃L=55.0°

What must the magnitude |𝐹B|
and direction 𝜃B
of the total force exerted on the book by the bottom of the bookshelf be in order for the book to remain in this position?
Relevant Equations
Fnet=ma
download.png


1.52cos(31)+Fbsin(Θb) = (0.305)(9.8)
Fbsin(Θb) = 1.69

Now for horizontal direction:
Fbcos(Θb) = FLsin(ΘL)
cos(Θb) = FLsin(ΘL)/Fb
cos(Θb) = (1.52 x sin31)/1.69

cosΘb=0.464
Θb = 62.35

I thought to find Fb I would just plug the Θb value into one of the trig functions, but apparently both of my answers are not right. What am I doing wrong?
 
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  • #2
It would help us help you if you used symbols instead of numbers. Failing that, at least you could tell us where the numbers you are using come from. For example, your first equation
1.52cos(31)+Fbsin(Θb) = (0.305)(9.8)
is totally mysterious to me.
Where did the force of 1.52, the angle of 31 and the mass of 0.305 come from? Put yourself in our position. We cannot help you find what you are doing wrong if we don't know what you are doing.
 
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  • #3
You seem to be working with two versions of the problem: different masses, different angles, different forces. One way that can happen is that a student cribs a solution to what looks like the same problem but fails to spot the differences in the numbers.
 
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Likes erobz

1. What causes a book to rest at an angle against one side of a bookshelf?

The angle at which a book rests against the side of a bookshelf is determined by the weight distribution of the book. If the book is heavier on one side, it will naturally tilt in that direction when placed on a flat surface.

2. Is it harmful for a book to rest at an angle against a bookshelf?

Resting at an angle against a bookshelf is not harmful for a book as long as the angle is not too extreme. However, over time, the spine of the book may become weakened or damaged if it is constantly stored at an angle.

3. Can a book be stored at an angle for a long period of time?

It is not recommended to store a book at an angle for a long period of time as it can cause damage to the spine and pages of the book. It is best to store books upright on a bookshelf or flat on a surface to maintain their structural integrity.

4. How can I prevent a book from resting at an angle on a bookshelf?

To prevent a book from resting at an angle on a bookshelf, make sure the shelf is level and sturdy. You can also use bookends or adjustable book supports to keep books upright and prevent them from tilting.

5. Are there any benefits to storing a book at an angle on a bookshelf?

There are no significant benefits to storing a book at an angle on a bookshelf. In fact, it can potentially lead to damage and distortion of the book's structure. It is best to store books in a flat or upright position to maintain their condition.

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