Let's solve the problems from the uploaded image step by step. I'll go through each part carefully:

(a) Find Young’s modulus of the muscle tissue

Given:

• Muscle length $L = 20 \, \text{cm} = 0.2 \, \text{m}$
• Extension $\Delta L = 3 \, \text{cm} = 0.03 \, \text{m}$
• Force required when relaxed $F = 25.0 \, \text{N}$
• Force required when tensed $F = 500 \, \text{N}$
• Cross-sectional area $A = 50 \, \text{cm}^2 = 5 \times 10^{-3} \, \text{m}^2$

Young’s modulus formula is: $E = \frac{\text{Stress}}{\text{Strain}} = \frac{F L}{A \Delta L}$

1. For relaxed muscles: $E_{\text{relaxed}} = \frac{25.0 \times 0.2}{5 \times 10^{-3} \times 0.03}$

2. For tensed muscles: $E_{\text{tensed}} = \frac{500 \times 0.2}{5 \times 10^{-3} \times 0.03}$

(b) Find $|\vec{F}_{\text{Forearm}}|$ and $|\vec{F}_{\text{Tendon}}|$:

Given:

• Weight of the dumbbell: $F_g = 200 \, \text{N}$
• Angle between $\vec{F}_{\text{Tendon}}$ and horizontal: $\theta = 80^\circ$
• The forces involved: $|\vec{F}_{\text{Tendon}}|$, $|\vec{F}_{\text{Forearm}}|$, and $F_g$.

Using torque equilibrium about the elbow joint: $\text{Sum of torques} = 0$ $F_g \times 40 \, \text{cm} = |\vec{F}_{\text{Tendon}}| \times 4 \, \text{cm} \times \cos(80^\circ)$

Solve for $|\vec{F}_{\text{Tendon}}|$. Then use force equilibrium (vertical): $|\vec{F}_{\text{Forearm}}| = F_g + |\vec{F}_{\text{Tendon}}| \sin(80^\circ)$

(c) Find $F_{\text{Deltoid}}$:

Given:

• Cable tension: $F_{\text{Naut}} = 40.0 \, \text{N}$
• Cable angle with forearm: $120^\circ$
• Deltoid attachment: $15.0 \, \text{cm}$
• Forearm length: $60.0 \, \text{cm}$
• Angle between deltoid and humerus: $170^\circ$

Using torque equilibrium about the shoulder joint: $F_{\text{Naut}} \times 60.0 \cos(120^\circ) = F_{\text{Deltoid}} \times 15.0 \cos(170^\circ)$

Solve for $F_{\text{Deltoid}}$.

Would you like a detailed step-by-step calculation for each part or assistance with anything specific?

Related Questions:

1. How does Young's modulus relate to the mechanical properties of a material?
2. What is the significance of torque in biomechanics problems?
3. Can you explain why static equilibrium conditions involve both torque and force balance?
4. How do the angles of forces influence the magnitude of resultant forces in mechanics?
5. Why is the deltoid muscle force higher than the cable tension in part (c)?

Tip:

Always check units carefully when plugging values into formulas to avoid calculation errors!