Question

A model weighing 45 kg is standing on a pencil heel each having an area of cross-section of 2 cm square. Calculate the pressure exerted on the floor.(Acceleration due to gravity-10m/s²)​

Answer 1

$\large \rm {\underbrace{\underline{⟴Elucidation:⤵}}}$

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$\qquad \qquad \tt \red {\underline{\underline{❍Provided:-}}}$

$\sf \to {Mass(m)=45kg}$

$\tt {Area(A)=2cm^{2}}$

$\sf \implies {[∵1m^{2}=1000cm^{2}]}$

$\sf \to {Area(A)=0.002m^{2}}$

$\sf \to {Acceleration(a)=10m/s^{2}}$

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$\qquad \qquad \tt \blue {\underline{\underline{❍To\: Find:-}}}$

$\sf \to {Pressure (p)=?}$

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$\qquad \qquad \tt \pink {\underline{\underline{❍We\: Know:-}}}$

$\sf \to {Pressure =\frac{Force}{Area}}$

$\tt \implies {\boxed{\boxed{P =\frac{F}{A}}}}$

➻But to Find Pressure,We need to find out the force.

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$\qquad \qquad \tt \purple {\underline{\underline{❍By\: definition:-}}}$

➻By the definition of force,it can be formulated as,

$\sf \to {Force=Mass×Acceleration}$

$\tt \implies {\boxed{F=m×a}}$

$\sf \to {F=45×10}$

$\sf \to {F=450kgm/s^{2}}$

$\tt \implies {\boxed{F=450N}}$

➻As we determined the force,we can now find the pressure.

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$\qquad \tt \orange {\underline{\underline{❍Final\: Substitution:-}}}$

$\large \sf \to {P =\frac{F}{A}}$

$\large \sf \to {P =\frac{450N}{0.0002m^{2}}}$

$\sf \to {P =\frac{450×10^{4}}{2}}$

$\large \sf \to {P =\frac{\cancel{450}^{225}×10^{4}}{\cancel{2}}}$

$\sf \to {P =225×10^{4}N/m^{2}}$

$\qquad \tt \implies \green {\boxed{\boxed{P =225×10^{4}pa}}}$

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