Suppose the point of insertion of the biceps muscle into the lower arm shown in (Figure 1) is 6.0 cm.
PART A
How much mass could the person hold with a muscle exertion of 520 N?
Express your answer to two significant figures and include the appropriate units
FIGURE
How Much Force Does Your Biceps Need to Hold 29kg?
The Problem
Let's calculate how hard your biceps works when holding a 29kg weight with your elbow bent at 105°. We know:
- Forearm + hand mass: 2.0 kg (CG 15cm from elbow)
- Held mass: 29 kg (35cm from elbow)
- Biceps attaches: 5.0cm from elbow
- Elbow angle: 105°
Key Physics Concept
Your elbow acts like a seesaw pivot. For equilibrium, the biceps torque must balance the torques from:
- Your forearm's weight
- The heavy weight you're holding
Torque Calculations
1. Forearm torque:
2.0kg × 9.81m/s² = 19.62N
19.62N × 0.15m = 2.943 Nm
2. Weight torque:
29kg × 9.81m/s² = 284.49N
284.49N × 0.35m = 99.5715 Nm
Total downward torque: 2.943 + 99.5715 = 102.5145 Nm
Biceps' Counter-Torque
The biceps pulls at 5cm from elbow, but the 105° bend reduces its effectiveness:
Effective lever arm = 5cm × sin(105°) = 0.05m × 0.9659 ≈ 0.0483m
The Final Calculation
For equilibrium: Biceps torque = Total downward torque
FM × 0.0483m = 102.5145 Nm
FM = 102.5145 ÷ 0.0483 ≈ 2120 N (or about 477 lbs of force!)
Why So Much Force?
Your biceps has terrible leverage because:
- It attaches very close to the elbow (just 5cm)
- The bent arm position reduces its effectiveness further
This is why lifting heavy weights with bent arms feels so difficult!
Real-World Takeaways
- Straighter arms give better leverage (require less muscle force)
- This explains proper lifting technique (use your legs, keep arms straighter)
- Your muscles can generate incredible forces despite poor leverage
The biceps needs to generate about 2120 N (477 lbs) of force to hold a 29kg weight with the elbow bent at 105°.
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