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 15.0 cm long, 6.00 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 16.1 cm , what is the tension T , in newtons, in the tendon?

Answer 1

The tension in the tendon is 2.9kN

Step-by-step explanation:

To solve the problem it is necessary to apply the concepts related to stress from the elongation of bodies by means of Young's Module.

The definition of Tension is given by

`F = AY(\Delta L)/(L_0)`

Where,

A =Area

Y = Young's modulus

`\Delta L =`Change in lenght

`L_0 =` Initial Lenght

The change in Length for this case is given by

`\Delta L` = 16.1-15 = 1.1cm

The area can be calculated as,

`A = \pi r^2`

`A = \pi (3*10^(-3))^2`

`A = 2.827*10^(-5)m^2`

Therefore replacing the tension would be,

`F = (2.827*10^(-5))(1.50×10^9)(1.1*10^(-2))/(16*10^(-2))`

`F = 2915.34N`

Therefore the tension in the tendon is 2.9kN