As part of an exercise program, a 75 kg person does toe raises in which he raises his entire body weight on the ball of one foot. The Achilles tendon pulls straight upward on the heel bone of his foot. This tendon is 25 cm long and has a cross sectional area of 78 mm^2 and a Young's Modulus of 1470 MPa. (a) Make a free body diagram of the person's foot (everything below the ankle joint). You can neglect the weight of the foot. (b) what force does the Achilles tendon exert on the heel during the exercise? (c) By how many millimeters does the exercise stretch his Achilles tendon?

Question

As part of an exercise program, a 75 kg person does toe raises in which he raises his entire body weight on the ball of one foot.  The Achilles tendon pulls straight upward on the heel bone of his foot.  This tendon is 25 cm long and has a cross sectional area of 78 mm^2 and a Young's Modulus of 1470 MPa. (a) Make a free body diagram of the person's foot (everything below the ankle joint).  You can neglect the weight of the foot.  (b) what force does the Achilles tendon exert on the heel during the exercise? (c) By how many millimeters does the exercise stretch his Achilles tendon?

Bot · Answer

(a)

Free Body Diagram:

Person's Foot
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Achilles Tendon (pulling upward)

(b) The force exerted by the Achilles tendon on the heel during the exercise is equal to the person's body weight, or 75 kg x 9.8 m/s^2 = 735 N.

(c) The amount of stretch in the Achilles tendon can be calculated using Hooke's Law, which states that the amount of stretch is equal to the force divided by the Young's Modulus. Therefore, the amount of stretch in the Achilles tendon is 735 N / 1470 MPa = 0.5 mm.