# 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
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

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?

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.

jbriggs444 and erobz
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.

erobz

## 1. What forces are acting on the book resting at an angle against the bookshelf?

There are three primary forces acting on the book: the gravitational force pulling it downward, the normal force exerted by the bookshelf supporting the book, and the frictional force between the book and the surface of the bookshelf which prevents it from sliding.

## 2. How can I calculate the angle at which the book is resting?

The angle can be calculated using trigonometric principles. If you know the height at which the top of the book touches the bookshelf and the length of the book, you can use the sine, cosine, or tangent functions to determine the angle.

## 3. What role does friction play in keeping the book in place?

Friction provides the necessary force to counteract the component of the gravitational force that would otherwise cause the book to slide down. The static friction between the book and the surface of the bookshelf must be sufficient to prevent motion.

## 4. How can I determine the coefficient of friction between the book and the bookshelf?

The coefficient of friction can be determined experimentally by gradually increasing the angle of the bookshelf until the book just begins to slide. At this critical angle, the tangent of the angle is equal to the coefficient of friction.

## 5. What happens if the angle is too steep for the book to stay in place?

If the angle is too steep, the component of the gravitational force parallel to the surface of the bookshelf will exceed the maximum static frictional force, causing the book to slide down the shelf.