Chapter 9, Problem 36P

If 25 kg is the maximum mass m that a person can hold in a hand when the arm is positioned with a 105° angle at the elbow as shown in Fig. 9-74, what is the maximum force F_max that the biceps muscle exerts on the forearm ? Assume the forearm and hand have a total mass of 2.0 kg with a _CG that is 15 cm from the elbow, and that the biceps muscle attaches 5.0 cm from the elbow.

To determine

The maximum force $F_{max}$ that the biceps muscle exerts on the forearm.

Answer to Problem 36P

Solution:

The maximum force $F_{max}$ that the biceps muscle exerts on the forearmis $1836\text{N}$ .

Explanation of Solution

Given:

Maximum mass placed in hand, $m=25\text{ kg}$

M₂ =2kg

Formula used:

The algebraic sum of all the moments should be zero

  ${\displaystyle \sum \tau =\overrightarrow{r}\times \overrightarrow{F}=0}$

Calculation:

Taking sum of all the moments about the joint:

  $\begin{array}{l}{\displaystyle \sum \tau }=0\\ F_{\max }(\sin 105°)(0.05)-2(9.8)(0.15)-25(9.8)(0.35)=0\\ 0.0483F_{\max }=88.69\\ F_{\max }=1836\text{N}\end{array}$

Conclusion:

The maximum force $F_{max}$ that the biceps muscle exerts on the forearmis $1836\text{N}$ .