Respuesta :
Answer:
[tex]F_b[/tex] = 1647.92 N
Explanation:
Given:
length of the arm, r = 0.465 m
distance of forearm from elbow, r' = 2.15 cm = 0.0215 m
Mass of the forearm, M = 2.45 kg
Mass of the object, m = 6.55 kg
Let, the Force by bicep be, [tex]F_b[/tex]
under the motionless condition, the net moment about elbow is zero
thus,
[tex]F_b[/tex] × 0.0215 - Mg × (0.465/2) - mg × (0.465) = 0
or
[tex]F_b[/tex] × 0.0215 - 2.45 × 9.8 × (0.465/2) - 6.55 × 9.8 × (0.465) = 0
or
[tex]F_b[/tex] × 0.0215 - 5.582 - 29.848 = 0
or
[tex]F_b[/tex] = 1647.92 N
hence, the force exerted by the elbow is 1647.92 N
This force exerted by the biceps muscles has been calculated as;
F_b = 1648 N
The image showing the bones of the forearm and biceps is missing and I have attached it.
We are given;
Length of forearm; L = 0.465 m
Mass of forearm; m_f = 2.45 kg
Mass of the object; m_o = 6.55 kg
Distance; d_f = 2.15 cm = 0.0215 m
- Under the equilibrium condition, we can calculate the force exerted by the biceps muscle by;
Taking moment about the elbow (E) and equating to zero, we have;
(F_b × d_f) - (m_f × g × L/2) - (m_o × g × L) = 0
Where F_b is the force exerted by the biceps muscles.
- Plugging in the relevant values, we have;
0.0215F_b - (2.45 × 9.8 × (0.465/2)) - (6.55 × 9.8 × 0.465) = 0
Rearranging gives;
0.0215F_b = (2.45 × 9.8 × (0.465/2)) + (6.55 × 9.8 × 0.465)
Multiplying out the bracket gives us;
0.0215F_b = 35.430675
F_b = 35.430675/0.0215
F_b ≈ 1648 N
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