Answer to Question #108545 in Physics for Roopali Jha

Question

Natural fibre reinforced PMMA is prepared for a biomedical application. The modulus of the fibre and PMMA are 200 and 5 GPa respectively. In order to achieve 160 GPa modulus how much fibre should be added (volume %) use mixture rule.

Answer 1

$$E_c=\frac{E_fE_{PMMA}}{E_fV_f+(1-V_f)E_{PMMA}}$$

$$160=\frac{(5)(200)}{200V_f+5(1-V_f)}$$

$$V_f=0.0064=0.64\%$$