Calculate the mass needed in order to suspend the leg shown in the figure(Figure 1) . Assume the leg (with cast) has a mass of 14.0 , and its CG is 34.0 from the hip joint; the sling is 81.5 from the hip joint.
To calculate the mass needed to suspend the leg shown in the figure, we can use the concept of moments. The principle of moments states that the sum of the clockwise moments is equal to the sum of the anticlockwise moments about a pivot point.
In this case, the pivot point is the hip joint, and we need to balance the moments. The clockwise moment is caused by the weight of the leg (including the cast), and the anticlockwise moment is caused by the force exerted by the sling.
Let's denote the mass needed to balance the moments as "m" (in kg).
The moment caused by the weight of the leg can be calculated using the formula:
Moment = Weight * Distance from the pivot point
The moment caused by the sling force can be calculated as:
Moment = Force * Distance from the pivot point
Setting up the equation:
Weight * Distance from the pivot point = Force * Distance from the pivot point
The weight of the leg (including the cast) is given as 14.0 kg, and its center of gravity (CG) is 34.0 cm from the hip joint.
The distance from the hip joint to the sling is given as 81.5 cm.
Substituting the given values into the equation, we get:
14.0 kg * 34.0 cm = m * 81.5 cm
Converting cm to meters, we have:
0.14 kg * 0.34 m = m * 0.815 m
Simplifying the equation, we get:
0.0476 kg m = 0.815 m * m
Now, we can solve for m by dividing both sides of the equation by 0.815 m:
0.0476 kg = m
Therefore, the mass needed to suspend the leg is approximately 0.0476 kg or 47.6 grams.