Approximately what force, FM, must the extensor muscle in the upper arm exert on the lower arm to hold a 7.9 kg shot put (Fig. 9-66)? Assume the lower arm has a mass of 2.8 kg and its CG is 11.2 cm from the pivot point.
To find the force (FM) exerted by the extensor muscle in the upper arm to hold the shot put, we need to consider the rotational equilibrium of the system.
Here's the step-by-step process to find the force exerted by the extensor muscle:
1. Calculate the gravitational force acting on the shot put:
Fg (gravitational force) = mass × acceleration due to gravity
Fg = 7.9 kg × 9.8 m/s^2
2. Determine the center of mass (CoM) of the system:
CoM = (mass of lower arm × distance of lower arm's CoG from the pivot point) + (mass of shot put × distance of shot put's CoG from the pivot point) / (mass of lower arm + mass of shot put)
CoM = (2.8 kg × 11.2 cm) + (7.9 kg × 0 cm) / (2.8 kg + 7.9 kg)
Note: The distance of the shot put's CoG from the pivot point is assumed to be zero since it is held by the lower arm.
3. Calculate the torque due to gravitational force:
Torque (τ) = gravitational force × distance of the CoM from the pivot point
τ = Fg × distance of CoM
4. Since the system is in rotational equilibrium, the torque due to the extensor muscle must balance the torque due to gravitational force:
Torque due to muscle force = τ
5. Write the equation for torque balance:
Torque due to muscle force = Torque due to gravitational force
FM × distance of the extensor muscle from the pivot point = τ
6. Solve for FM:
FM = τ / distance of the extensor muscle from the pivot point
Now, you have the process to find the force (FM) exerted by the extensor muscle in the upper arm. Just substitute the appropriate values into the equations and perform the necessary calculations.