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If the 20-mm-diameter rod is made of a-36 steel and the stiffness of the spring is k = 67 mn/m , determine the displacement of end a when the 60-kn force is applied. take e = 200 gpa

Sagot :

The displacement at the end of A is 1.09 mm

According to the question,

Rod's diameter, d= 20 mm

Stiffness constant, k = 55 M-N/m or,

                                 = 55 × 10⁶ N/m

Force, f = 60 kN or,

            = 60 × 10³ N

Young's modulus, E = 200 Gpa or,

                                = 200 × 10⁹ pa

We know the formula,

A=[tex]\pi d^2 /4[/tex]

By substituting the values,

     = [tex]\pi (0.02)^{2} /4[/tex]

=0.0003 m³

length, L =A×E/K

=1.14 m

hence,

The displacement be:

60×10³×1.14/0.0003×200×10³×10³×10³=1.09 mm

Displacement is  1.09 mm

Learn more about force here:

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#4264

The displacement of end a is 1.09mm

given:

Rod diameter,d=20mm

stiffness constant,k=55mn/m

force,f=60kn

young modulus,E= 200gpa

we know the formula

[tex]\pi \: d {}^{2} /4[/tex]

By substituting values in the above formula

[tex] = \pi(0.02) {}^{2} /4[/tex]

[tex] = 0.0003m {}^{3} [/tex]

length L=A×E/K

=1.14m

Hence, displacement is

[tex]60 \times 10 {}^{3} \times 1.14 \times/0.0003 \times 200 \times 10 {}^{3} \times 10 {}^{3} \times 10 {}^{3} [/tex]

=1.09mm

learn more about displacement from here: https:/brainly.com/question/28167908

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