- #1
pixietree
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Homework Statement
A human holds a ball of mass 8kg at his hand, so that the forearm is perpendicular to the upperarm.
The distance between the elbow and the center of mass of the forearm is 0.15 meters, the distance between the elbow and the muscle is 0.05 meters and the mass of the forearm is 2 kg. The ball is held 0.35 meters from the elbow (as depicted below).
Find the force of the mustle given equilibrium.
Homework Equations
$$\sum_{i=1}^n \tau_i=0$$
$$F_{m} = ma$$
The Attempt at a Solution
$$r_{mustle}*F_{mustle} - r_{arm}*F_{arm} - r_{ball}*F_{ball}=0$$
$$F_{mustle} = \frac {r_{arm}*F_{arm} + r_{ball}*F_{ball}}{r_{mustle}}$$
Hence, $$F_{mustle} = \frac {r_{arm}*m_{arm}+r_{ball}*m_{ball}}{r_{mustle}} *g $$
Setting the given data yields $$\mathbf F = 608.22\mathbf y N$$
Here is the part I don't understand: If I am right, the forearm does not move and hence does not accelerate.
But $$F-m_{arm}*g-m_{ball}*g = 608.22 - 2*9.81 - 8*9.81 = 510.12 N$$, hence the sum of forces on the formarm is not zero.