Question

The largest tendon in the body, the Achilles tendon, connects the calf muscle to the heel bone of the foot. This tendon is typically 13.0 cm long, 5.60 mm in diameter, and has a Young's modulus of 1.50×109 Pa . If an athlete has stretched the tendon to a length of 13.9 cm , what is the tension ? , in newtons, in the tendon?  

Answer 1

Length of the tendon = L = 13 cm = 0.13 m.

Elongation made by the athlete = L = ( 13.9 - 13 ) cm = 0.9 cm = 0.009 m.

Diameter of the tendon = 5.6 mm.

Hence, its radius = r = 5.6 mm / 2 = 2.8 mm = 0.0028 m.

Hence, area of cross - section = A = r² = 3.14 x 0.0028² m² = 2.46 x 10^-5 m².

Hence, Young's modulus = Y = ( T / A ) / ( L / L ) = ( TL ) / ( A L )

or, T = ( YA L ) / L = ( 1.5 x 10⁹ x 0.009 x 2.46 x 10^-5 / 0.13 ) N

or, T = 2.55 x 10³ N.