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Found in: Page 82

### Matter & Interactions

Book edition 4th edition
Author(s) Ruth W. Chabay, Bruce A. Sherwood
Pages 1135 pages
ISBN 9781118875865

# A system is acted upon by two forces, $<18,47,-23>\mathrm{N}\phantom{\rule{0ex}{0ex}}$and $<-20,-13,41>\mathrm{N}$ . What is the net force acting on the system?

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

See the step by step solution

## Step 1: 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.

## Step 2: Calculation for the net force

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

Add both the given forces as

${\stackrel{\mathbf{\to }}{\mathbf{F}}}_{\mathbf{net}}\mathbf{}\mathbf{=}\stackrel{\mathbf{\to }}{{\mathbf{F}}_{\mathbf{1}}}\mathbf{}\mathbf{+}\mathbf{}\stackrel{\mathbf{\to }}{{\mathbf{F}}_{\mathbf{2}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{Substitute}\mathbf{}\mathbf{the}\mathbf{}\mathbf{values}\mathbf{}\mathbf{in}\mathbf{}\mathbf{the}\mathbf{}\mathbf{above}\mathbf{}\mathbf{expression}\mathbf{.}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}{\stackrel{\mathbf{\to }}{\mathbf{F}}}_{\mathbf{net}\mathbf{}}\mathbf{}\mathbf{=}\mathbf{<}\mathbf{18}\mathbf{,}\mathbf{47}\mathbf{,}\mathbf{-}\mathbf{23}\mathbf{>}\mathbf{N}\mathbf{}\mathbf{+}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{20}\mathbf{,}\mathbf{-}\mathbf{13}\mathbf{,}\mathbf{41}\mathbf{>}\mathbf{N}\mathbf{.}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{18}\mathbf{>}\mathbf{N}\mathbf{.}\phantom{\rule{0ex}{0ex}}\mathbf{Therefore}\mathbf{,}\mathbf{}\mathbf{the}\mathbf{}\mathbf{net}\mathbf{}\mathbf{force}\mathbf{}\mathbf{acting}\mathbf{}\mathbf{on}\mathbf{}\mathbf{the}\mathbf{}\mathbf{system}\mathbf{}\mathbf{is}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{2}\mathbf{,}\mathbf{34}\mathbf{,}\mathbf{18}\mathbf{>}\mathbf{N}\mathbf{.}\phantom{\rule{0ex}{0ex}}$