Question #110177
15 mm dia SS (Young’s modulus = 200 Gpa) rod is coated with HA (Young’s modulus = 300 Gpa).
A) What should be the coating thickness so that the Young’s modulus of the composite is 210 Gpa (use mixture rule)?
B) If the densities are 7.9 and 4.0 gm/cc, what is the average density?
1
Expert's answer
2020-04-20T15:11:23-0400

We know that, for the composite material


Yc=Y1V1+Y2V2Y_c= Y_1V_1+Y_2V_2


Here , Y1,Y2Y_1, Y_2 are the young modulus for composite material and V1 and V2 are the

volume here length will be same only cross sectional area is changing



210(15+x)2=152×200+(x)2×300210(15+x)^2=15^2\times 200 +(x)^2\times300

47250+210x2+6300=45000+300x247250 +210 x^2+6300=45000+300x^2


90x26300x2250=090x^2-6300x-2250=0


x270x25=0x^2-70x-25=0


x=0.35 mm

(ii) For average density we have formula as


δav=δ1×δ2δ1x1+δ2x2\delta_{av}=\frac{\delta_1\times\delta_2}{\delta_1x_1 +\delta_2x_2}


δav=7.9×4.07.9×15+4×.35\delta_{av}=\frac{7.9\times4.0}{7.9\times15+4\times.35}


δav=0.238gcm3\delta_{av}=0.238 \frac{g}{cm^3}



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