Solve Shear Stress Problem: Cartilage Deformed at 7.4°

[M_J]

Homework Statement

The force on a knee cartilage can cause a large force to deform it. The cartilage area is 11cm^2 and the shear modulus is 12MPa. Max force at impact is 904N at an angle of 12 degrees with the cartilage, through what angle (in degrees) will the cartilage be deformed?

Homework Equations

http://session.masteringphysics.com/problemAsset/1026529/6/yg.11.35.jpg

Shear modulus = Stress/Strain

Stress = F(perpendicular)/A

Strain = x/h

The Attempt at a Solution

Stress = 904sin(12)/11x10^-4

Strain = 0.0142

h=11x10-2 ??

angle = tan^-1(0.0142/11x10-2) = 7.4

This method appears a little wrong, is someone able to point out where I have gone wrong and how I should have got to the answer? Thanks! :-)

 

[SteamKing]

Your calculations are also units-free, which makes them even more difficult to follow.

 

[M_J]

All units are SI, stress has units of Pa, strain is a ratio so has no units and h is measured in metres. My angle is in degrees.

I would be grateful if you were now able to help me with my answer! :-)

 

[Chestermiller]

All units are SI, stress has units of Pa, strain is a ratio so has no units and h is measured in metres. My angle is in degrees.

I would be grateful if you were now able to help me with my answer! :-)

Your angle calculation is incorrect. You already have the shear strain, so why are you dividing by the area?

Chet

 

[M_J]

Thanks, can you explain what I do need to do then please?

 

[M_J]

Don't worry, I have done it now - thanks anyway!

 

[M_J]

Your calculations are also units-free, which makes them even more difficult to follow.

Thanks!

 

[bpennkast]

Don't worry, I have done it now - thanks anyway!

what exactly did you do to change your original setup? i can't figure this one out