Two muscles in the back of the leg pull upward on the Achilles tendon, as shown in Figure 4.40. (These muscles are called the medial and lateral heads of the gastrocnemius muscle.) Find the magnitude and direction of the total force on the Achilles tendon. What type of movement could be caused by this force?

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Ciara Beatrice CanalitaLv10

14 Nov 2020

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The upper leg muscle exerts a force of 1200N, Which is carried by tendon over the kneecap at the angles shown in the figure. Find the direction and magnitude of the force exerted by the kneecap on the upper leg bone(the femur)?

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When a person stands on tiptoe (a strenuous position), the position of the foot is as shown in Figure (a). The total gravitational force on the body, g, is supported by the force exerted by the floor on the toes of one foot. A mechanical model of the situation is shown in Figure (b), where is the force exerted by the Achilles tendon on the foot and is the force exerted by the tibia on the foot. Find the values of , , and ? when g = 695 N.

The tangential force method involves finding the component of the applied force that is perpendicular to the displacement from the pivot point to where the force is applied. This perpendicular component of the force is called the tangential force.

(a) What is , the magnitude of the tangential force that acts on the pole due to the tension in the rope?

Express your answer in terms of

and

.

When using the tangential force method, you calculate the torque using the equation

$\tau = f_{\rm t} d$ ,

where

is the distance from the pivot to the point where the force is applied. The sign of the torque can be determined by checking which direction the tangential force would tend to cause the pole to rotate (where counterclockwise rotation implies positive torque).

(b) What is the magnitude of the torque

on the pole, about point A, due to the tension in the rope?

Express your answer in terms of

, and

The moment arm method involves finding the effective moment arm of the force. To do this, imagine a line parallel to the force, running through the point at which the force is applied, and extending off to infinity in either direction. You may shift the force vector anywhere you like along this line without changing the torque, provided you do not change the direction of the force vector as you shift it. It is generally most convenient to shift the force vector to a point where the displacement from it to the desired pivot point is perpendicular to its direction. This displacement is called the moment arm.

For example, consider the force due to tension acting on the pole. Shift the force vector to the left, so that it acts at a point directly above point A in the figure. The moment arm of the force is the distance between the pivot and the tail of the shifted force vector. The magnitude of the torque about the pivot is the product of the moment arm and force, and the sign of the torque is again determined by the sense of the rotation of the pole it would cause.