When the mass is removed, the length of the cable is found to be l0 = 4.66 m. After the mass is added, the length is remeasured
1 answer:
Answer:
Explanation:
For a linear elastic material Young's modulus is a constant that is given by:
Here, F is the force exerted on an object under tensio, A is the area of the cross-section perpendicular to the applied force, is the amount by which the length of the object changes and
is the original length of the object. In this case the force is the weight of the mass:
Replacing the given values in Young's modulus formula:
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We are asked to determine the force required by the neck muscle in order to keep the head in equilibrium. To do that we will add the torques produced by the muscle force and the weight of the head. We will use torque in the clockwise direction to be negative, therefore, we have:
Since we want to determine the forces when the system is at equilibrium this means that the total sum of torque is zero:
Now, we solve for the force of the muscle. First, we add the torque of the weight to both sides:
Now, we divide by the distance of the muscle:
Now, we substitute the values:
Now, we solve the operations:
Therefore, the force exerted by the muscles is 23.53 Newtons.
Part B. To determine the force on the pivot we will add the forces we add the vertical forces:
Since there is no vertical movement the sum of vertical forces is zero:
Now, we add the force of the muscle and the weight to both sides to solve for the force on the pivot:
Now, we plug in the values:
Solving the operations:
Therefore, the force is 73.53 Newtons.