Chapter 9, Problem 2P

To determine

The mass needed to suspend the leg.

Answer to Problem 2P

Solution: Mass of the load is 6.73 kg needed to suspend the leg.

Explanation of Solution

Given:

The mass of the leg, M = 15.0 kg

The distance between the CM of leg & hip joint, D = 0.35 m.

The distance between the hip joint and the sling, L = 0.78 m

Formula Used:

  $MgD=F_{T}L$ .

  $F_T$ is the force on the sling and g is the acceleration due to gravity.

Calculation:

The force on the sling of the leg is:

  $\begin{array}{c}{F}_T=\frac{MgD}{L}\\ =\frac{\text{(}15\text{kg)(}9.8{\text{m/s}}^{\text{2}}\text{)(}0.35\text{m)}}{\text{(}0.78\text{m)}}\\ =65.96\text{N}\end{array}$

There is no acceleration of the hanging mass:

Thus,

  $\begin{array}{c}{F}_T=mg\\ m=\frac{F_T}{g}\\ =\frac{\text{65}\text{.96}\text{N}}{9.8{\text{ m/s}}^2}\\ =6.73\text{kg}\end{array}$

Conclusion: Mass of the load is 6.73 kg needed to suspend the leg.