*please walk me through equation
The patellar tendon attaches to the tibia at the tibial tuberosity. The tibial tuberosity is 7 cm from the center of the knee joint. The patellar tendon pulls at an angle of 35deg to the line passing through the tibial tuberosity and the center of the knee joint.
If the patellar tendon produces an extension torque around the knee joint equal to the 400Nm.
How large is the force in the patellar tendon?
To find the force in the patellar tendon, we can use the concept of torque. Torque is calculated by multiplying the force applied by the distance from the point of rotation. In this case, the point of rotation is the knee joint.
1. Convert the angle from degrees to radians: Since trigonometric functions use radians, we need to convert the angle from degrees to radians.
- Angle in radians = Angle in degrees * (π/180)
- Angle in radians = 35 * (π/180) = 0.61 radians
2. Find the perpendicular distance from the line passing through the tibial tuberosity and the center of the knee joint to the line of action of the force in the patellar tendon. This distance is the projection of the line passing through the tibial tuberosity and the knee joint center onto the line of action of the force.
- Distance = 7 cm * cos(angle in radians)
- Distance = 7 * cos(0.61) = 4.91 cm
3. Calculate the force in the patellar tendon using the equation for torque:
- Torque = Force * Distance
- Force = Torque / Distance
- Force = 400 Nm / (4.91 cm * 0.01 m/cm) = 816.71 N
Therefore, the force in the patellar tendon is approximately 816.71 Newtons.
To find the force in the patellar tendon, we need to use the principle of torque. Torque is calculated by multiplying the force applied by the distance from the point of rotation.
In this case, we have the extension torque produced by the patellar tendon, which is given as 400 Nm. We also know that the tibial tuberosity is 7 cm (or 0.07 m) away from the center of the knee joint.
Now, let's calculate the force in the patellar tendon using trigonometry. We have the angle between the line passing through the tibial tuberosity and the center of the knee joint, which is 35 degrees.
Step 1: Calculate the perpendicular distance from the line passing through the tibial tuberosity and the center of the knee joint to the line of action of the force in the patellar tendon. This distance is equal to the product of the given distance (0.07 m) and the sine of the angle (35 degrees).
Perpendicular distance = 0.07 m x sin(35 degrees) ≈ 0.04 m
Step 2: Now, we can find the force in the patellar tendon by dividing the extension torque by the perpendicular distance calculated in Step 1.
Force in the patellar tendon = Extension torque / Perpendicular distance
= 400 Nm / 0.04 m
= 10,000 N
Therefore, the force in the patellar tendon is approximately 10,000 Newtons.