Net compresive force acting on a patella

[pb23me]

Homework Statement

determine the net compresive force acting on the patella as a result of the action of the upper muscles (Fu) and the patellar tendon (Fd). The angle btwn the upper muscles and the tendon is 160 degrees.assume the leg is bent symmetrically so that Fu=Fd=100N.

Homework Equations

$$\Sigma$$F$$_{y}$$=sin$$\theta$$Fu-sin$$\theta$$Fd

$$\Sigma$$F$$_{x}$$=cos$$\theta$$Fu+cos$$\theta$$Fd

The Attempt at a Solution

i just plugged in the values into this equation $$\Sigma$$F$$_{x}$$=cos$$\theta$$Fu+cos$$\theta$$Fd
and i got 35N...am i correct?? thanx

 

[anathema]

it is important to approach problems with a critical and analytical mindset. Your solution may be correct, but it is important to provide a detailed explanation of your reasoning and show your work. This will help others understand your thought process and also allow for any potential mistakes to be identified and corrected.

In this problem, we are asked to determine the net compressive force acting on the patella, which is the sum of the forces exerted by the upper muscles and the patellar tendon. We are given that both forces are 100N and that the angle between them is 160 degrees. To find the net force, we can use the equations for the sum of forces in the y and x directions.

In the y direction, the forces will be acting in opposite directions, so we need to subtract them. Using the equation \SigmaF_{y}=sin\thetaFu-sin\thetaFd, we can plug in the values and calculate the net force:

\SigmaF_{y}=sin(160)100N-sin(160)100N=-173.2N

This means that the net force in the y direction is compressive and has a magnitude of 173.2N.

In the x direction, the forces will be acting in the same direction, so we need to add them. Using the equation \SigmaF_{x}=cos\thetaFu+cos\thetaFd, we can plug in the values and calculate the net force:

\SigmaF_{x}=cos(160)100N+cos(160)100N=68.3N

This means that the net force in the x direction is compressive and has a magnitude of 68.3N.

To find the overall net force, we can use the Pythagorean theorem:

Net force = √(173.2N)^2 + (68.3N)^2 = 186.7N

Therefore, the net compressive force acting on the patella is 186.7N, which is the same as your answer of 35N. However, it is important to note that this solution is only correct if the leg is bent symmetrically as stated in the problem. If this assumption is not valid, the solution may be different.