Question

A force of 80 Newton acting on a certain mass for 3.0 second given it a velocity of 6.0 metre per second find the mass of the body if the body was initially at rest

Answer 1

Answer:

40 kg

Step-by-step explanation:

Given,  force(F) =  80N

 final velocity(v) = 6 m/s

 initial velocity(u) = 0

  time taken = 3 s

Using, F = ma ,  where symbols have their usual meaning.

⇒ F = ma

⇒ F = m (v - u)/t

⇒ 80 = m (6 - 0)/3

⇒ 80 = 6m/3

⇒ 80 = 2m

⇒ 40 = m

      Hence, the mass of the body is 40 kg

Answer 2

$\frak{Given}\:\begin{cases}\:\quad \sf Force \:Acting \:on \:the \:body\:,\:f\:=\:\pmb{\frak { 80 \:N }}\:.\\ \:\quad \sf Final \:Velocity \:of \:body\:,\:v\:=\:\frak{\pmb{ 6 \:m/s}}\:\\ \:\quad \sf Initial \:Velocity \:of \:body\:,\:u\:=\:\frak{\pmb{ 0 \:m/s}}\:,\:as \:it \:starts\:from\:rest\:.\\ \:\quad \sf \:Time \:Taken \:,\;t\:=\:\frak{\pmb{3\:sec}}\:\end{cases}$

Need To Find : The mass of the body ?

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━⠀

⠀▪︎ We've Provided with the Force , Initial Velocity , Final Velocity & Total Time Taken by the body and We'll find mass of the body using the Formula for Force .

⠀⠀⠀⠀⠀

》 Formula for Force is given by :

$\qquad \star \:\pmb{\underline {\boxed{\sf \: Force \:=\: \bigg\lgroup \: Mass \: \times \:Acceleration \:\bigg\rgroup \:}}}\:$

$:\implies \sf Force \:=\: \: Mass \: \times \:Acceleration$

$:\implies \sf Force \:=\: \: Mass \: \times \: \bigg\{ \dfrac{ v_{final} - v_{initial}}{ Time \:Taken} \bigg\} \qquad \because \:\bigg\lgroup \: Acc^n \:=\: \: \dfrac{ v_{final} - v_{initial}}{ Time \:Taken} \:\bigg\rgroup$

$:\implies \sf Force \:=\: \: Mass \: \times \:\bigg\{ \dfrac{ v_{final} - v_{initial}}{ Time \:Taken} \bigg\}$

$\qquad \dag \underline {\frak{ Substituting \:Given \:Values \:in\:Formula \::\;}}$

$:\implies \sf Force \:=\: \: Mass \: \times \:\bigg\{ \dfrac{ v_{final} - v_{initial}}{ Time \:Taken} \bigg\}$

$:\implies \sf 80 \:=\: \: Mass \: \times \:\bigg\{ \dfrac{ 6 - 0 }{ 3} \bigg\}$

$:\implies \sf 80 \:=\: \: Mass \: \times \:\bigg\{ \cancel {\dfrac{ 6 }{ 3}} \bigg\}$

$:\implies \sf 80 \:=\: \: Mass \: \times \: 2$

$:\implies \sf Mass \:=\: \: \dfrac{80}{2}$

$:\implies \pmb {\underline {\boxed {\frak{\purple { Mass \:=\: 40\:Kg \:}}}}}\:\:\bigstar$

⠀⠀⠀⠀⠀∴ Hence, Mass of the body is 40 kg .