IMG_20190118_135204.jpg (7) Two parallel and opposite forces, each 4,000 N are applied tangentially to the upper and lower faces of a cubical metal block 25 cm on a side. Find the angle of shear and the displacement of the upper surface relative to the lower surface. Shear modulus for the metal is 80 GPa. (4)A mass of 2 kg is suspended from a steel wire of length 1 meter to form a pendulum arrangement. Of the mass is moved to one side and released from the horizontal position of wire then find the maximum extension in the length of the wire.

Answers (2)
S safeer

angle  of shear strain 

\theta=\frac{F}{AG}=\frac{4000}{0.0625\times8\times10^{10}}=8\times10^{-7}\\\Delta l=l\theta=0.25\times8\times10^{-7}=2\times10^{-7}

S safeer

velocity at lowest position =√2g=√2*10=√20 m/s        ,∴g=10m/s^2

now force at lowest position F=mg+0.5mv^2/r=2g+2*20/1=  2*10+40  = 20+40    = 60 N

Y=60/10^-6/ΔL/1  

2×10^11=60/ΔL*10^-6

60/2*×10^11*10^-6=ΔL

ΔL=3*10^-4 m

ΔL=0.3 mm 

 

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