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Expert-verified Found in: Page 82 ### Matter & Interactions

Book edition 4th edition
Author(s) Ruth W. Chabay, Bruce A. Sherwood
Pages 1135 pages
ISBN 9781118875865 # A truck driver slams on the brakes and the momentum of the truck changes from${\mathbf{<}}{\mathbf{65}}{\mathbf{,}}{\mathbf{000}}{\mathbf{,}}{\mathbf{0}}{\mathbf{,}}{\mathbf{0}}{\mathbf{>}}{\mathbf{}}{\mathbf{kg}}{\mathbf{.}}{\mathbf{m}}{\mathbf{/}}{\mathbf{s}}{\mathbf{}}{\mathbf{to}}{\mathbf{<}}{\mathbf{26}}{\mathbf{,}}{\mathbf{000}}{\mathbf{,}}{\mathbf{0}}{\mathbf{,}}{\mathbf{0}}{\mathbf{>}}{\mathbf{}}{\mathbf{kg}}{\mathbf{.}}{\mathbf{m}}{\mathbf{/}}{\mathbf{s}}$ ${\mathbf{in}}{\mathbf{}}{\mathbf{4}}{\mathbf{.}}{\mathbf{1}}{\mathbf{}}{\mathbf{s}}{\mathbf{}}{\mathbf{}}$due to a constant force of the road on the wheels of the truck. As a vector, write the net force exerted on the truck by the surroundings.

The net force exerted on the truck by the surrounding is $<-9512.2,0,0>\mathrm{N}$.

See the step by step solution

## Step 1: Definition and the formula of the net force

The rate of change of a particular system’s momentum will be equated to the net force applied to that system.

If the system's momentum changes from initial momentum $\stackrel{\to }{{\mathrm{p}}_{1}}$ to final momentum $\stackrel{\to }{{p}_{2}}$ over time $\mathbf{∆}\mathbf{T}$ , the force acting on the system will be,

localid="1653963994357" style="max-width: none; vertical-align: -17px;" $\underset{{\mathbf{F}}_{\mathbf{n}\mathbf{e}\mathbf{t}}}{\mathbf{\to }}{\mathbf{}}{\mathbf{=}}\frac{\stackrel{\mathbf{\to }}{{\mathbf{p}}_{\mathbf{2}}}\mathbf{}\mathbf{-}{\stackrel{\mathbf{\to }}{\mathbf{p}}}_{\mathbf{1}}}{\mathbf{∆}\mathbf{t}}$

## Step 2: Finding the net force on the system.

Substitute $<65,000,0,0>\mathrm{kg}.\mathrm{m}/\mathrm{s}$ for $\underset{{p}_{1}}{\to }$ , $<26,000,0,0>\mathrm{kg}.\mathrm{m}/\mathrm{s}$ for $\underset{{p}_{2}}{\to }$ , and $4.1s$for $∆\mathrm{t}$ into the formula of the net force acting on the system.

role="math" localid="1653965078905" $\stackrel{\mathbf{\to }}{{\mathbf{F}}_{\mathbf{n}\mathbf{e}\mathbf{t}}}\mathbf{}\mathbf{=}\frac{\mathbf{<}\mathbf{26}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{kg}\mathbf{.}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}\mathbf{}\mathbf{-}\mathbf{<}\mathbf{65}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{kg}\mathbf{.}\mathbf{}\mathbf{m}\mathbf{/}\mathbf{s}}{\mathbf{4}\mathbf{.}\mathbf{1}\mathbf{s}}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{<}\mathbf{26}\mathbf{,}\mathbf{000}\mathbf{-}\mathbf{65}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{0}\mathbf{-}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{-}\mathbf{0}\mathbf{>}\mathbf{kg}\mathbf{.}\mathbf{m}\mathbf{/}\mathbf{s}}{\mathbf{4}\mathbf{.}\mathbf{1}\mathbf{s}}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{<}\mathbf{-}\mathbf{39}\mathbf{,}\mathbf{000}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{}\mathbf{kg}\mathbf{.}\mathbf{m}\mathbf{/}\mathbf{s}}{\mathbf{4}\mathbf{.}\mathbf{1}\mathbf{s}}\mathbf{}\mathbf{.}\mathbf{\left(}\begin{array}{c}\mathbf{1}\mathbf{N}\\ \mathbf{1}\mathbf{kg}\mathbf{.}\mathbf{m}\mathbf{/}\mathbf{s}\end{array}\mathbf{\right)}\phantom{\rule{0ex}{0ex}}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{=}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{9512}\mathbf{.}\mathbf{2}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{N}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{Therefore}\mathbf{,}\mathbf{}\mathbf{the}\mathbf{}\mathbf{net}\mathbf{}\mathbf{force}\mathbf{}\mathbf{on}\mathbf{}\mathbf{the}\mathbf{}\mathbf{system}\mathbf{}\mathbf{is}\mathbf{}\mathbf{}\mathbf{<}\mathbf{-}\mathbf{9512}\mathbf{.}\mathbf{2}\mathbf{,}\mathbf{0}\mathbf{,}\mathbf{0}\mathbf{>}\mathbf{N}\mathbf{.}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}$ ### Want to see more solutions like these? 