The chewing muscle, the masseter, is one of the strongest in...

The chewing muscle, the masseter, is one of the strongest in the human body. It is attached to the mandible (lower jawbone) as shown in Figure P8.33a. The jawbone is pivoted about a socket just in front of the auditory canal. The forces acting on the jawbone are equivalent to those acting on the curved bar in Figure $P 8.33 \mathrm{b} . \overrightarrow{\mathbf{F}}_{C}$ is the force exerted by the food being chewed against the jawbone, $\overrightarrow{\mathbf{T}}$ is the force of tension in the masseter, and $\overrightarrow{\mathbf{R}}$ is the force exerted by the socket on the mandible. Find $\overrightarrow{\mathbf{T}}$ and $\overrightarrow{\mathbf{R}}$ for a person who bites down on a piece of steak with a force of 50.0 N.

The chewing muscle, the masseter, is one of the strongest in the human body. It is attached to the mandible (lower jawbone) as shown in Figure P8.33a. The jawbone is pivoted about a socket just in front of the auditory canal. The forces acting on the jawbone are equivalent to those acting on the curved bar in Figure $P 8.33 \mathrm{b} . \overrightarrow{\mathbf{F}}_{C}$ is the force exerted by the
food being chewed against the jawbone, $\overrightarrow{\mathbf{T}}$ is the force of tension in the masseter, and $\overrightarrow{\mathbf{R}}$ is the force exerted by the socket on the mandible. Find $\overrightarrow{\mathbf{T}}$ and $\overrightarrow{\mathbf{R}}$ for a person who bites down on a piece of steak with a force of 50.0 N.

Key Concepts

Lever Mechanics

Lever mechanics is the study of how forces are distributed and translated through a object that rotates about a pivot or fulcrum. It involves analyzing the distances from the pivot (moment arms) at which the forces act, allowing for the determination of the effective force amplification or reduction.

Static Equilibrium

Static equilibrium refers to the condition where the sum of all forces and the sum of all moments (torques) acting on a body are zero. This concept is fundamental in analyzing systems where objects are at rest or moving at a constant speed, ensuring that there is no net force or rotational acceleration.

Free Body Diagram

A free body diagram is a simplified representation of an object, isolated from its surroundings, that shows all external forces and moments acting on it. This tool is essential for systematically analyzing the interactions and applying the equilibrium conditions to solve for unknown forces.

Moment (Torque) Analysis

Moment analysis involves calculating the turning effect produced by a force acting at a distance from a pivot point. By multiplying the force by its moment arm, this concept helps in ensuring rotational equilibrium, which is crucial for solving force distribution problems in mechanical systems.

Transcript

00:01 Hi there.

00:02 So for this problem, we need to calculate the force of tension in the mass stature and the force asserted by the socket on the mandible.

00:15 And so this picture in here represent all of the forces that are opting on the jaw, the jaw bone, and f of s represents.

00:31 Sense in the force that the food, the force asserted by the food and when it is being shoot against the job on.

00:43 So we are given that that force in this case, we are trying to buy down a piece of steak with a force of 50 newton's.

00:56 So to solve this problem, we are going first to use newton's second law, to assume all of the forces that are opting on the job on, and after that, applying the same, but for the torques.

01:13 And in this case, we are going to set that the point of rotation is on the point that is being applied the force t, so that we can set that the torque in that point is zero.

01:29 So with that said, first, we are going to to use newton's second law to sum all of the forces.

01:37 So in this case, we only have forces in the y company, as you can see in the picture.

01:44 And it is the negative force minus f, c, the force exerted by the food, plus the positive force t minus the force r, which, as you can, see in the picture is pointing downward and this should be equals to zero because we are in the equilibrium the system is not moving so in here we will have this first equation and we will also have the sum of torts and in this case as i said in the beginning we said that the the point here in green is the point of rotation.

02:47 And it coincides with the point of application of the force t so that the torque produced by this 4t is equal to zero because the distance to the force of application is zero.

03:03 So we will obtain that zero.

03:06 But for the other forces is different because we have a distance that is given also in the exercise.

03:13 A distance of 70 .5 centimeters to the force that is being asserted by the food and a distance of 3 .5 centimeters to the distance to the force or to the point of application of the force it's asserted by the socket which is the force art.

03:43 So that we know that the torque is defined as, well, the magnitude of the torque is defined as the r distance to the point of application of the force times the force times the sign of the angle that is between the vector r and the position vector r and the vector force.

04:20 So in this case, you can see that all of these vectors, this vector are and this vector are for angle of 90 degrees...

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