Difficult# Shear Slope

CLMECH-EIGRXG

The plank below makes an angle of 30° above horizontal. The plank has a compressive strength of $4.2\cdot 10^7\,Pa$, the shear strength is $9.58\cdot 10^6\,Pa$, and a cross-sectional area of $1.29\cdot 10^{-2}\,m^2$. The plank is supported by rollers embedded in the front and back edges of the wall which are horizontally separated by 10 cm.

The end of the plank abuts a third roller which prevents it from sliding through the other rollers. The distance Jeff walks up the plank is measured from the point where the plank contacts the roller support beneath the plank. The weight of the plank can be ignored. The length of the plank is 20 m.

Jeff weighs 890 N. How far up the rough plank can Jeff walk until the plank gives way?