Question

$\huge \bf Question$

● A hammer of mass 500g, moving at 50ms‐¹, strikes a nail. The nail stops the hammer in a very short time of 0.01s. What is the force of the nail on the hammer.

▪︎Note:-

Wrong answer will reported on spot..!!!​

Answer 1

Topic

Impulse

Given

A hammer of mass 500g, moving at 50m/s strikes a nail. The nail stops the hammer in a very short time of 0.01s.

To Find

What is the force of the nail on the hammer ?

Concept Used

Impulse

The total impact by a force within a duration is known as Impulse.

Formula

Impulse = Force × Time

Impulse = Change in Momentum

Force × Time = m∆v

Solution

It is given that

Mass of Hammer, m = 500 g

Mass of Hammer, m = 0.5 kg

Initial velocity of Hammer, u = 50 m/s

Final velocity of Hammer, v = 0 m/s

( as hammer stops after striking )

The nail stops in time = 0.01 s

Apply formula,

Force × Time = m( v - u )

Force × 0.01 = (0.5)( 0 - 50 )

Force = 100 × ( - 25 )

Force = -2500 N

So, force of nail on hammer is -2500 N.

Negative sign shows the direction of Force, so magnitude of Force will be 2500 N.

Answer

So, force of nail on hammer is 2500 N ( in magnitude ).

Note :

Another method could be like shown below,

F = ma

F = m( v - u) / t

Put the values and value will be -2500 N again.

Taking magnitude answer will be 2500 N.

Answer 2

${\underline{\underline{\rm{Given:}}}}$

• Mass of Hammer = 500g = 0.5 kg
• Initial Velocity = 50 m/s
• Final velocity = 0 m/s
• Time taken = 0.01 sec

${\underline{\underline{\rm{To \: find :}}}}$

• Force of the nail on the hammer.

${\underline{\underline{\rm{Solution :}}}}$

Here we have to first find Accleration of the hammer and by applying the formula of Force we will get the Force required.

● Acceleration of the Hammer is :-

${\underline{\boxed{\sf{ Final \: velocity = Initial \: velocity + Acceleration \times Time}}}}$

${\underline{\boxed{\sf{ \longrightarrow v=u + a(t) }}}}$

${\ratio{\longmapsto{\sf{0 = 50 + a(0.01)}}}} \\ \\ {\ratio{\longmapsto{\sf{ - 50 = a(0.01)}}}} \\ \\ {\ratio{\longmapsto{\sf{ \cfrac{ - 50}{0.01} = a}}}} \\ \\ {\ratio{\longmapsto{\sf{a = \cfrac{ - 50 \: \: }{ \cfrac{1}{100} } }}}} \\ \\ {\ratio{\longmapsto{\sf{ a = - 50 \times 100}}}} \\ \\ { \boxed{\ratio{\longmapsto{\sf{Acceleration = - 5000 \: ms^{ - 2} }}}}}$

$\rule{300}{2}$

● So, Force required is :-

${ \boxed{\ratio{\longmapsto{ \sf{Force = Mass \times Acceleration}}}}}$

${ \boxed{\ratio{\longmapsto{ \sf{F = m \times a}}}}}$

$\large{\sf{\ratio{\longmapsto{Force = 0.5 \times (-5000)}}}} \\ \\ { \underline{ \boxed{ \red{\large{\sf{\ratio{\longmapsto{Force = - 2500 \: Newton }}}}}}}}$

So, Force of the nail on the hammer is -2500 N.