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# As seen , collar $D$ is released from rest and slides without friction downward a distance of $h=300 \mathrm{~mm}$ where it strikes a head fixed to the end of compound rod $A B C$. Rod segment (1) is made of aluminum $\left[E_1=70 \mathrm{GPa}\right.$, and it has a length of $L_1=800 \mathrm{~mm}$ and a diameter of $d_1=12 \mathrm{~mm}$. Rod segment (2) is made of bronze [ $\left.E_2=105 \mathrm{GPa}\right]$, and it has a length of $L_2=1,300 \mathrm{~mm}$ and a diameter of $d_2=16 \mathrm{~mm}$. What is the allowable mass for collar $D$ if the maximum normal stress in the aluminum rod segment must be limited to $200 \mathrm{MPa}$ ?

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Given:

• Height: $h=300\text{ mm}$;
• Modulus of elasticity: $E_1=70\ \mathrm{GPa}$;
• Length: $L_1=800\text{ mm}$;
• Diameter: $d_1=12\text{ mm}$;
• Modulus of elasticity: $E_2=105\ \mathrm{GPa}$;
• Length: $L_2=1300\text{ mm}$;
• Diameter: $d_2=16\text{ mm}$;
• Maximum normal stress: $\sigma_{\text{max}}=200\text{ MPa}$;

Required:

• Collar mass.

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