you are required to conduct a direct shear experiment, the following data are collected for a direct shear test conducted on a cohesionless soil sample named "Animo LaSand":

Specimen dimensions: diameter $=71mm$; height $=25mm$

Normal stress: $150k\frac{N}{m^2}$

Shear force at failure: $276$ N

a$.)$ Determine the angle of friction of the sand sample.

b$.)$ For a normal stress of $200k\frac{N}{m^2},$ what shear force is required to cause failure?

c$.)$ If a direct shear test is conducted with a normal force of $675$ N $,$ what would be the principal stresses at failure?