## Step 1: **Calculate the Extension (\(\Delta L\)) Using's Modulus** The formula for under a force using Young's modulus: \[ Delta L = \fracF L_}{A Y} \Where: - \(F = \,N\) (force) - \(L_ = 6.9\,cm = .069\,m\) (original length) - \(A = \pi r^2 = \pi (.002\,m)^2 = 1.257 \times 10^{-5}\,m^2\) (cross-sectional area) - \(Y = 1.5 \times 10^9\,N/m^2\) (Young's modulus) Plug in values: \[ \Delta L = \frac{100 \times .069}{1.257 \times 10^{-5} \times 1.5 \times 10^9} \] \[ A = \pi \times (.002)^2 = \pi \times .000004 = .00001257\,m^2 \] \[ \Delta L = \frac{69}{.00001257 \times 1.5 \times 10^9} \] \[ = \frac{69}{18855} \] \[ = .00366\,m \approx 3.66\,mm \] **Explanation:** We calculated the extension (\(\Delta L\)) of the tendon under a 100 N load using the Young's modulus relationship. --- ## Step 2: **Find the Stretched Length** The new length under load is: \[ L = L_ + \Delta L \] \[ L = .069\,m + .00366\,m = .07266\,m \] **Explanation:** We add the extension to the original length to get the total stretched length of the tendon. --- ## **Final Answer** \[ \boxed{.0727\,m} \] **The length of the quadricep tendon under a 100 N load is approximately** \(.0727\,m\) **(or 7.27 cm).**

# Step 1: **Calculate the Extension (\(\Delta L\)) Using Young's Modulus** To find the extension (\(\Delta L\)) of the quadricep tendon under a force, we use the formula: \[ \Delta L = \frac{F L_0}{A Y} \] Where: - \(F = 1000\,N\) (force) - \(L_0 = 6.9\,cm = 0.069\,m\) (original unstretched length) - \(A = \pi r^2\) (cross-sectional area) - \(Y = 1.5 \times 10^9\,N/m^2\) (Young's modulus) First, calculate the cross-sectional area \(A\): \[ A = \pi (0.002\,m)^2 = \pi \times 0.000004\,m^2 \approx 1.25664 \times 10^{-5}\,m^2 \] Now plug in the values to calculate \(\Delta L\): \[ \Delta L = \frac{1000 \times 0.069}{1.25664 \times 10^{-5} \times 1.5 \times 10^9} \] \[ = \frac{69}{18840.96} \approx 0.00366\,m \approx 3.66\,mm \] **Explanation:** We calculated the extension (\(\Delta L\)) of the tendon under a 1000 N load using the Young's modulus relationship and found it to be approximately 3.66 mm. --- # Step 2: **Find the Stretched Length** To find the total length of the tendon under load, we add the extension to the original length: \[ L = L_0 + \Delta L \] \[ L = 0.069\,m + 0.00366\,m \approx 0.07266\,m \] **Explanation:** We added the calculated extension to the original length to determine the total stretched length of the tendon. --- ## **Final Answer** \[ \boxed{0.07266\,m} \] **The length of the quadricep tendon under a 1000 N load is approximately** \(0.0727\,m\) **(or 7.27 cm).**