How Do Forces Affect the Deformation and Young's Modulus of a Book?

[Schoomy]

Homework Statement

A large book has forces of magnitude 14 N applied in opposite directions to two opposite faces of area 42 cm². The thickness of the book (L) is 2.0 cm. The deformation angle (g) is 8.4°.

1) what is change in X?
2) What is young's modulus for the book?

http://dl.getdropbox.com/u/119186/Picture%201.png

Homework Equations

I tried getting change in x doing 2cos(8.4) but I'm horrible at trig. What should I have done?

Once I do that, I can just plug it all into F/A = S*deltaX/L
Right?

What should I be doing to get the change in X?

 

[Schoomy]

And I should have just used SIN!

Can someone explain to me why I needed to use SIN over COS in this example? I just don't get it.

What does SIN or COS intrinsically mean, represent, etc?

 

[nlightner]

To determine the change in X, you need to use the formula Δx = L tan(θ), where L is the thickness of the book and θ is the deformation angle. In this case, the change in X would be 0.29 cm.

To calculate the Young's modulus for the book, you can use the formula E = F/AΔx/L, where F is the force applied, A is the area of the book, Δx is the change in X, and L is the thickness of the book. In this case, the Young's modulus would be approximately 97.9 N/cm^2.

It is important to note that this calculation assumes the book is a homogeneous material and that the forces are evenly distributed across the surface. Realistically, the book may have varying densities and the forces may not be evenly distributed, so the calculated Young's modulus may not be entirely accurate.