Even when the head is held erect, as in the figure below, its center of mass is not directly over the principal point of support (the atlanto-occipital joint, point A). The muscles at the back of the neck should therefore exert a force to keep the head erect. That is why your head falls forward when you fall asleep in the class. If the head weighs 43 N, calculate the force exerted by the muscles, FM, using the information in the figure.
I have no idea how to even begin solving this problem. If someone could help me out and maybe even just give me some direction or outline the steps that would be awesome!
To solve this problem, you need to use the principle of torque equilibrium. Torque is the tendency of a force to rotate an object around a specific point, and it is calculated by multiplying the force by the perpendicular distance from the point of rotation to the line of action of the force.
Here's how you can approach this problem step-by-step:
Step 1: Draw a free-body diagram. Draw a diagram of the head, showing the weight force (43 N) acting vertically downward from the center of mass, and the force exerted by the muscles (FM) acting upward at the back of the neck.
Step 2: Identify the point of rotation. In this case, the point of rotation is the atlanto-occipital joint (point A).
Step 3: Determine the perpendicular distance. Measure the distance between the atlanto-occipital joint (point A) and the line of action of the force exerted by the muscles (FM). This distance represents the lever arm.
Step 4: Set up the torque equation. Torque equilibrium occurs when the net torque acting on the head is zero. In this case, the torque due to the weight force is balanced by the torque due to the muscle force. The torque equation can be written as:
Torque due to weight force = Torque due to muscle force
Step 5: Calculate the torque due to the weight force. Torque is calculated by multiplying the weight force (43 N) by the perpendicular distance from the atlanto-occipital joint (point A) to the line of action of the weight force.
Step 6: Solve for the force exerted by the muscles (FM). Rearrange the torque equation and solve for FM. Substitute the known values from the problem, such as the torque due to the weight force and the perpendicular distance. Calculate FM.
By following these steps, you should be able to calculate the force (FM) exerted by the muscles at the back of the neck to keep the head erect.