Chapter 9, Problem 6P

Figure 9-50 shows a pair of forceps used to hold a thin plastic rod firmly. If the thumb and finger each squeeze with a force Ft = F_f= 11 0 N, what force do the forceps jaws exert on the plastic rod?

Figure 9-50

To determine

Amount of force the jaws of forceps exert on the plastic rod.

Answer to Problem 6P

Solution:34.62 N

Explanation of Solution

Given:

The thumb and finger each squeeze with equal force i.e. $F_T=F_F=11.0\text{N}$ .

Total length of forceps jaw = $\text{(2}\text{.70) cm }$

Formula Used: Torque: $\tau =F\times r=Fr\sin \theta$

Net torque = 0 because system is in equilibrium.

Calculation:

The force is acting perpendicular to the point of rotation,

  $\begin{array}{l}\therefore \theta ={\text{90}}^{\circ }\\ \sin {90}^{\circ }=1\end{array}$

  $\begin{array}{l}{F}_1{r}_1=F_2{r}_2\\ \left(11.0\text{N}\right)(0.085{\text{m)=F}}_2(0.027\text{m)}\\ \Rightarrow {\text{F}}_2=34.62\text{N}\end{array}$

Conclusion: Amount of force the jaws of forceps exert on the plastic rod = 34.62 N.