A subject with a height of 165cm and mass of 69 kg is sitting with his lower limb positioned with hip in 90 degree of flexion and knee in full extension and foot in 90 degree of dorsiflexion
a) calculate the inter-segment force at the knee joint
b)Calculate the net external moment about the knee joint
c) Calculate the force in the patella tendon, given that it acts horizontally with a lever arm of 4 cm about the centre of the joint
d)The joint force at the knee joint
e) Comment on the difference in the inter-segment force and the joint force at the knee joint
did u manage to work this out?
a) To calculate the inter-segment force at the knee joint, we can use the principle of equilibrium. The force at the knee joint will be equal to the weight of the lower limb. Since the mass of the subject is 69 kg and the acceleration due to gravity is approximately 9.8 m/s^2, the weight can be calculated as follows:
Weight = mass * acceleration due to gravity
Weight = 69 kg * 9.8 m/s^2
Weight ≈ 676.2 N
Therefore, the inter-segment force at the knee joint is approximately 676.2 N.
b) The net external moment about the knee joint can be calculated using the equation:
Net External Moment = Inter-segment force * lever arm
Given that the foot is in 90 degrees of dorsiflexion, the lever arm from the knee joint to the foot is the distance from the knee joint to the ankle joint. Assuming this distance is 40 cm (0.4 m), the net external moment can be calculated as follows:
Net External Moment = 676.2 N * 0.4 m
Net External Moment ≈ 270.48 Nm
Therefore, the net external moment about the knee joint is approximately 270.48 Nm.
c) The force in the patella tendon can be calculated using the equation:
Force = Net External Moment / lever arm
Given that the lever arm is 4 cm (0.04 m) about the center of the joint, the force in the patella tendon can be calculated as follows:
Force = 270.48 Nm / 0.04 m
Force ≈ 6762 N
Therefore, the force in the patella tendon is approximately 6762 N.
d) The joint force at the knee joint can be calculated by summing all the forces acting on the joint. In this case, there are two forces: the inter-segment force (676.2 N) and the force in the patella tendon (6762 N).
Joint Force = Inter-segment force + Force in patella tendon
Joint Force = 676.2 N + 6762 N
Joint Force ≈ 7438.2 N
Therefore, the joint force at the knee joint is approximately 7438.2 N.
e) The difference between the inter-segment force and the joint force at the knee joint is that the inter-segment force only accounts for the weight of the lower limb, while the joint force takes into consideration both the weight of the lower limb and the force in the patella tendon. The joint force is higher than the inter-segment force because it also includes the additional force generated by the contraction of the quadriceps muscle acting on the patella tendon.
To answer the questions, we need to consider the biomechanics of the subject's lower limb and apply relevant equations. I'll explain how to approach each question step by step:
a) To calculate the inter-segment force at the knee joint, we need to consider the equilibrium of forces acting on the lower limb. The force can be calculated using the equation:
Force at the knee = (Mass x Acceleration) + Inter-segment force
Here, we know the subject's mass (69 kg), but we don't have information about the acceleration. Assuming the subject is at rest (not accelerating), the equation simplifies to:
Force at the knee = Inter-segment force
So, the inter-segment force at the knee joint of the subject can be approximated to be equal to the force at the knee joint.
b) To calculate the net external moment about the knee joint, we need to consider the moments caused by the forces acting on the limb. The equation for moment is:
Moment = Force x Moment arm
The force we are interested in is the inter-segment force at the knee joint (approximately the same as the force at the knee joint). The moment arm is the distance between the axis of rotation (knee joint) and the line of action of the force. Unfortunately, the specific distance is not provided in the question, so we can't calculate the exact net external moment.
c) The force in the patella tendon can be calculated using the equation:
Force = Moment / Lever arm
Here, the moment is obtained from the previous question (net external moment about the knee joint), and the lever arm (distance between the center of the joint and the line of action of the force) is specified as 4 cm in the question. Plug in the values to calculate the force in the patella tendon.
d) The joint force at the knee joint is the same as the inter-segment force at the knee joint (as discussed in question a). So, you can use the same value.
e) The inter-segment force and the joint force at the knee joint are expected to be quite similar, as mentioned in question a. However, without more specific information or calculations, it is challenging to comment further on the exact difference between these forces.
Please note that these calculations are based on certain assumptions and may not be entirely accurate without additional information. It's always better to consult a professional in the field for a more precise analysis of biomechanical forces.