Question

Last week in homework 8 you calculated the force that the Achilles tendon applies to the heel in order to stabilize the foot when standing on tiptoes. Assuming that this force is approximately 1300 N, calculate the amount by which the Achilles tendon will stretch when you are standing on tiptoes if it is 15 cm long, has a cross-sectional area of 105 mm 2, and its Young’s modulus is 0.2 ×1010 N/ m2. (5 Points)

Answer 1

here total load = 1300 N are applied on tiptoes,

area of tiptoes = A = 105 mm² = 105 x 10^-6 m² { here 1 mm = 10^-3 m , 1 mm² = 10^-6 m² }

length of tiptoes = 15 cm = 0.15 m { 1 m = 100 cm }

young's modulus E = 0.2 x 10¹⁰ N/m²

so here we want to find Achilles tendon stretch ,

so here stretch means small deflection ,

so we have deflection formula,

d = P l / A E

here d = deflection = stretch

d = PL / AE

= 1300 x 0.15 / (105 x 10^-6 x  0.2 x 10¹⁰)

= 195 / 21 x 10⁴

d= 9.2857 x 10^-4 m

this answer is meter unit , if we convert it into milli meter,

1 m = 10³ milli meter

so 9.258 x 10^-4 m = 9.258 x 10^-4 x 10³ milli meter

= 9.258 x 10^-1 mm

d = 0.925 mm

so Achilles tendon will stretch about   d = 0.925 mm