Chapter 2, Problem 26A

Consider two forces, one having a magnitude of 20 N and the other a magnitude of 12 N. What is the maximum net force possible for these two forces? The minimum?

To determine

Maximum and minimum net force possible.

Answer to Problem 26A

  $F_{\text{max}}=32\text{N}$ and $F_{\text{min}}=8\text{N}$

Explanation of Solution

Given:

The given forces are,

  $F_1=20\text{N}$ and $F_2=12\text{N}$

Formula used:

The maximum force is given as,

  $F_{\max }=F_1+F_2$

The minimum force is given as,

  $F_{\min }=F_1-F_2$

Calculation:

For maximum net force, the two forces must act in same direction.

So,

  $\begin{array}{l}{F}_{\text{max}}=F_1+F_2\\ =20+12\\ \Rightarrow F_{\text{max}}=32\text{N}\end{array}$

For minimum net force, the two forces must act in opposite direction.

So,

  $\begin{array}{l}{F}_{\text{min}}=F_1-F_2\\ =20-12\\ \Rightarrow F_{\text{min}}=8\text{N}\end{array}$

Conclusion:

Therefore, the maximum net force possible is $F_{\text{max}}=32\text{N}$ and minimum net force possible is $F_{\text{min}}=8\text{N}$