A wire of length 2.50m with a cross section area of 3.5 times 10^-6 m^2 stretche

Question

A wire of length 2.50m with a cross section area of 3.5 times 10^-6 m^2 stretches by 2.1cm when a load of 1850 N is hung from it. What is the young's modulus for this wire? An aluminum support team is 2.00m long; it has a cross sectional shape of a perfect square, each side of that square b 3.00cm. The beam is fixed at one end and a force perpendicular to the length is applied to the unfixed end. The force deflects the beam 5.50cm at the point of contact from the force. What is the magnitude of the force? (use the table 9.2 in the book to find the appropriate Modulus) If the force in part b is applied by and object that has the same contact area as the cross sectional area as the beam, what is the pressure on the beam from the object?

Explanation / Answer

a)   Young Modulus = FLo/Aox

                                = (1850 * 2.50)/ (3.5 * 10-6 * 0.021 )

                                 = 6.2925 * 1010 N/m2

b)     Here,   deflection = (FL3)/(3EI)

                  => 0.0550 = F *( 2)3/ (3 * 69 * 109 * 0.034/12 )      

=> F =     96.06 N -------------------> magnitude of force

c)    Pressure on the beam = F/A

   = 96.06/(0.03 * 0.03)      =    106733.33 N/m2

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