Question

A system is acted upon by two forces, $<18,47,-23>\mathrm{N}$and$<-20,-13,41>\mathrm{N}$. What is the net force acting on the system?

Short answer

The net force acting on the system is$<-2,34,18>\mathrm{N}.$

Step-by-step solution

Understanding the definition of the net force

A force is described as a push or pull on an object that occurs due to the interaction of one system with a different system. When two items interact, each of them experiences a force.

Calculation for the net force

To calculate the net force acting on this system, combine all forces.

Add both the given forces as

$$\begin{gathered} {\overrightarrow{\mathbf{F}}}_{\mathbf{net}}\mathbf{}\mathbf{=}\overrightarrow{{\mathbf{F}}_{\mathbf{1}}}\mathbf{}\mathbf{+}\mathbf{}\overrightarrow{{\mathbf{F}}_{\mathbf{2}}} \\ \mathbf{Substitute}\mathbf{}\mathbf{the}\mathbf{}\mathbf{values}\mathbf{}\mathbf{in}\mathbf{}\mathbf{the}\mathbf{}\mathbf{above}\mathbf{}\mathbf{expression}\mathbf{.} \\ {\overrightarrow{\mathbf{F}}}_{\mathbf{net}\mathbf{}}\mathbf{}\mathbf{=}\mathbf{<}\mathbf{18}\mathbf{,}\mathbf{47}\mathbf{,}\mathbf{-}\mathbf{23}\mathbf{>}\mathbf{N}\mathbf{}\mathbf{+}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{20}\mathbf{,}\mathbf{-}\mathbf{13}\mathbf{,}\mathbf{41}\mathbf{>}\mathbf{N}\mathbf{.} \\ \mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{18}\mathbf{>}\mathbf{N}\mathbf{.} \\ \mathbf{Therefore}\mathbf{,}\mathbf{}\mathbf{the}\mathbf{}\mathbf{net}\mathbf{}\mathbf{force}\mathbf{}\mathbf{acting}\mathbf{}\mathbf{on}\mathbf{}\mathbf{the}\mathbf{}\mathbf{system}\mathbf{}\mathbf{is}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{18}\mathbf{>}\mathbf{N}\mathbf{.} \end{gathered}$$