A patient rehabilitating a knee injury performs knee extension exercises wearing a 20 N ankle weight. Calculate the amount of torque generated at the knee by the weight boot for four positions, given a distance of 0.5 m between the weight’s center of gravity and the knee joint center.At θ= 30°
Question
A patient rehabilitating a knee injury performs knee extension exercises wearing a 20 N ankle weight. Calculate the amount of torque generated at the knee by the weight boot for four positions, given a distance of 0.5 m between the weight’s center of gravity and the knee joint center.At θ= 30°
Solution
To calculate the torque, we use the formula:
Torque = Force x Distance x sin(θ)
where:
- Force is the force applied, which is 20 N in this case.
- Distance is the distance from the point of application of the force to the axis of rotation, which is 0.5 m in this case.
- θ is the angle between the force vector and the lever arm, which is 30° in this case.
First, we need to convert the angle from degrees to radians because the trigonometric functions in the formula work with radians.
1 degree = 0.0174533 radians
So, 30 degrees = 30 * 0.0174533 = 0.523599 radians
Now we can substitute the values into the formula:
Torque = 20 N x 0.5 m x sin(0.523599 radians) = 5 Nm
So, the amount of torque generated at the knee by the weight boot at θ= 30° is 5 Nm.
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