Question

025 A mechanic strikes a nail with a hammer of mass 400g moving with a velocity of
20m/s the hammer comes to rest in 0.04sec after striking the nail. Calculate the force
ented by the nail calculate the force by the nail on the hammer

Answer 1

$\Large\bf{\color{indigo}GiVeN,}$

• Mass of a hammer is 400g.

$\longmapsto\:\:\bf\blue{Mass\:(m)\:=\:400\:g\:=\:0.4\:kg}$

• Initial velocity of hammer is 20 m/s.

$\longmapsto\:\:\bf\purple{Initial\:velocity\:(u)\:=\:20\:m/s}$

• Final velocity of hammer is 0 m/s (Rest).

$\longmapsto\:\:\bf\pink{Final\:velocity\:(v)\:=\:0\:m/s}$

• Time period is 0.04 s.

$\longmapsto\:\:\bf\green{Time\:(t)\:=\:0.04\:s}$

$\bf\orange{We\:know\:that,}$

$\red\bigstar\:\:{\underline{\green{\boxed{\bf{\color{peru}v\:=\:u\:+\:a\:t\:}}}}}$

$\bf\red{Where,}$

• a is acceleration of the hammer.

$\longrightarrow\:\:\bf{0\:=\:20\:+\:a\times{0.04}\:}$

$\longrightarrow\:\:\bf{0.04\:a\:=\:-\:20\:}$

$\longrightarrow\:\:\bf{a\:=\:\dfrac{-20}{0.04}\:}$

$\longrightarrow\:\:\bf{a\:=\:-\dfrac{2000}{4}\:}$

$\longrightarrow\:\:\bf\gray{a\:=\:-\:500\:m/s^2\:}$

[NOTE :- Here negative sign indicates that the hammer is moved backward direction, because after strikes to nail a backward force act's on the hammer. That's why acceleration acts also in backward direction. It is also known as retardation.]

$\bf\blue{We\:know\:that,}$

$\pink\bigstar\:\:{\underline{\purple{\boxed{\bf{\color{olive}Force\:(F)\:=\:mass\times{acceleration}\:}}}}}$

$:\implies\:\:\bf{F\:=\:0.4\times{500}\:}$

$:\implies\:\:\bf\green{F\:=\:200\:N}$

$\Large\bold\therefore$ The force exerted by the nail on hammer is 200 N.