HW QUESTION-PLEASE HELP!

Question

When you bend your knee, the quadriceps muscle is stretched. This increases the tension in the quadriceps tendon attached to your kneecap (patella), which, in turn, increases the tension in the patella tendon that attaches your kneecap to your lower leg bone (tibia). Simultaneously, the end of your upper leg bone (femur) pushes outward on the patella. The figure shows how these parts of a knee joint are arranged. What size force does the femur exert on the kneecap if the tendons are oriented as in the figure and the tension in each tendon is 60 N?

NOTES: the angle is 42' and the figure looks like one arrow coming straight up from the patella and the patella tendon (another arrow) points down to the right. (I tried including the figure but it went over the character limit)

Answer 1

Hi Lauren M.

To find the force that the femur exerts on the kneecap, we can analyze the forces acting in the knee joint. It's important to consider the angle at which the tendons are oriented. We can use trigonometry to solve for the force.

Let's denote:

- T1 as the tension in the quadriceps tendon (60 N).

- T2 as the tension in the patella tendon (also 60 N).

- θ as the angle between T1 and T2, which is given as 42 degrees.

We want to find the force exerted by the femur (F) on the kneecap.

We can break down the forces into their horizontal (Fx) and vertical (Fy) components. The force exerted by the femur on the kneecap is in the horizontal direction.

Using trigonometry, we can relate the forces as follows:

Fy (vertical) = T1 + T2 * sin(θ)

Fx (horizontal) = T2 * cos(θ)

Substitute the known values:

Fy = 60 N + 60 N * sin(42°)

Fy = 60 N + 60 N * 0.6691

Fy ≈ 40.146 N

Now, to find F (the force exerted by the femur on the kneecap), use the Pythagorean theorem:

F^2 = Fx^2 + Fy^2

F^2 = (T2 * cos(θ))^2 + Fy^2

F^2 = (60 N * cos(42°))^2 + (40.146 N)^2

Calculate F:

F ≈ √((60 N * cos(42°))^2 + (40.146 N)^2)

F ≈ √(1511.406 N^2 + 1611.313 N^2)

F ≈ √(3122.719 N^2)

F ≈ 55.869 N

So, the femur exerts a force of approximately 55.869 N on the kneecap.

I hope this will help. I am happy to tutor you on any other questions you may have; please feel free to send me a message!