A 15-cm-long tendon was found to stretch 3.7 mm by a force of 13.4 N. The tendon was approximately round with an average diameter of 8.5 mm. Calculate Young’s modulus of this tendon.

9.57

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To calculate Young's modulus, we can use the equation:

Young's modulus (E) = stress / strain

First, let's calculate the stress using the formula:

stress = force / area

The area of the tendon can be calculated using the formula for the area of a circle:

area = π * (radius)^2

Given that the average diameter of the tendon is 8.5 mm, the radius would be half of that, which is 4.25 mm or 0.425 cm. Thus, the area is:

area = π * (0.425 cm)^2

Now, let's calculate the strain using the formula:

strain = change in length / original length

The change in length is given as 3.7 mm, and the original length is 15 cm.

Finally, we can substitute these values into the equation for Young's modulus:

Young's modulus (E) = (force / area) / (change in length / original length)

Young's modulus (E) = [(13.4 N) / (π * (0.425 cm)^2)] / [(3.7 mm) / (15 cm)]

Computing this expression will give us the value of Young's modulus for the tendon.

To calculate Young's modulus of the tendon, we first need to know the formula for Young's modulus:

Young's modulus (Y) = stress (σ) / strain (ε)

In this case, stress is the force applied (13.4 N) and strain is the change in length of the tendon (3.7 mm).

Step 1: Calculate the stress
To find the stress in the tendon, we need to convert the force to the area. Since the tendon is approximately round, we can use the formula for the area of a circle:

Area (A) = π * (radius)^2

The average diameter given is 8.5 mm, so the radius (r) is half of that: 8.5 mm / 2 = 4.25 mm.

Now, let's convert the radius to meters: 4.25 mm / 1000 = 0.00425 m.

Substitute the values into the area formula: A = π * (0.00425 m)^2

Next, calculate the stress by dividing the force by the area: σ = 13.4 N / A

Step 2: Calculate the strain
The strain is the change in length divided by the original length. In this case, the original length is 15 cm = 150 mm.

Substitute the values into the formula: ε = (Change in length) / (Original length) = 3.7 mm / 150 mm.

Step 3: Calculate Young's modulus
Finally, substitute the stress and strain values into the formula for Young's modulus: Y = σ / ε

Now, you can calculate the value of Young's modulus using the values obtained from the previous steps.