BIO Tendon-Stretching Exercises. 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 (?Fig. P11.59?). 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 mm2 and a Young’s modulus of 1470 MPa. (a) Draw a free-body diagram of the person’s foot (everything below the ankle joint). Ignore the weight of the foot. (b) What force does the Achilles tendon exert on the heel during this exercise? Express your answer in newtons and in multiples of his weight. (c) By how many millimeters does the exercise stretch his Achilles tendon?

Solution Step 1 of 3: (a) Draw a free-body diagram of the person’s foot (everything below the ankle joint). Ignore the weight of the foot. A m= 75 kg person has his tendon l=25 cm=0.25m long and cross sectional area A=78 mm =78× 10 6 m having young’s modulus of Y=1470 MPa=1470 × 10 Pa. Here in 6 part (a) we need to write the free body diagram for the ankle when the person raises his entire body weight on the ball of one foot. The free body diagram for the ankle is, Step 2 of 3: (b) What force does the Achilles tendon exert on the heel during this exercise Express your answer in newtons and in multiples of his weight. In order to calculate the force exerted by the achilles tendon on the heel during the exercise , we need to use the definition of torque That is, F × d = mgh From the given figure d= 4.6 cm and h =12.5 cm F(4.6 cm ) = mg(12.5 cm) F=2.72 mg 2 Substituting m= 75 kg and g=9.8 m/s 2 F = 2.72 (75 kg)(9.8 m/s ) F= 2000 N Therefore, the force exerted on the heel is F= 2000 N = 2.72 mg.