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  • Two parallel and opposite forces, each 4,000 N are applied tangentially to the upper and lower faces of a cubical metal block 2

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.

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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}

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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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Safeer PP

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