Answer to Question #155119 in Physics for Arvin Shopon

Question

The gymnast supports a 20 kg dumbbell as shown. Calculate how much force the biceps muscle applies to the forearm of the forearm. The attachment point of the biceps in the spindle is 5 cm and the center of the dumbbell is 30 cm from the elbow joint. The own weight of the forearm does not need to be considered.

 

Answer 1

We have two torques acting on the forearm: the force of gravity of the dumbbell acts downward with corresponding torque and the bicep force acts upward creating a corresponding torque. To hold the dumbbell, the torques must be in equilibrium:

$$\tau_1=\tau_2,\\ F_1d_1=F_2d_2,\\ m_1gd_1=F_2d_2,\\\space\\ F_2=\frac{m_1gd_1}{d_2}=\frac{20\cdot9.8\cdot0.3}{0.05}=1176\text{ N}.$$