Question

A hammer of mass 500g, moving with 50ms-1, strikes a nail . the nai stops the hammer in a very short time of 0.01s,what is the force of the nail on the hammer
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Answer 1

$\underline {\underline{ \large \mathtt {\green{Given}}}}$

• mass of the hammer = 500 g = 0.5 kg

• initial velocity of the hammer = 50 m/s

• final velocity of the hammer = 0 m/s

• time taken for the hammer to stop = 0.01 sec

$\underline {\underline{ \large \mathtt {\blue{To \: find}}}}$

• force acting on the nail by the hammer

$\underline {\underline{ \large \mathtt {\pink{concept}}}}$

• In order to find the force applied by the hammer on the nail we need the mass of the hammer and the acceleration of the hammer
• In order to find acceleration we will use the first kinematic equation

$\underline {\underline{ \large \mathtt {\orange{solution}}}}$

As per the first kinematic equation ,

$\bigstar \large\mathtt{ \boxed{v = u + at}}$

here ,

• v = final velocity
• u = initial velocity
• a = acceleration
• t = time taken

Substituting the given values in the above equation ,

$\rightarrow \mathtt{u = - at}$

$\rightarrow \mathtt{a = - \dfrac{u}{t} }$

$\rightarrow \mathtt{a = - \dfrac{50}{0.01} }$

$\rightarrow \mathtt{ \red{a = - 5000 \dfrac{m}{ {s}^{2} } }}$

Note : here negative sign denotes retardation

_________________________

We know that ,

$\bigstar \large\mathtt{ \boxed{f = ma}}$

here ,

• f = force
• m = mass
• a = acceleration

Substituting the given values in the above equation ,

$\rightarrow \mathtt{f = 0.5 \times 5000}$

$\rightarrow \mathtt{ \red{f =2500N}}$

Force acting on the nail by the hammer is 2500 N

$\underline {\underline{ \large \mathtt {additional \: formulas}}}$

second kinematic equation ,

$\bigstar \large\mathtt{ \boxed{ \purple{s = ut + \dfrac{1}{2} a {t}^{2} }}}$

_______________________

third kinematic equation ,

$\bigstar \large\mathtt{ \boxed{ \purple{ {v}^{2} = {u}^{2} + 2as }}}$

_______________________

$\bigstar \large\mathtt{ \boxed{ \purple{s = u + \frac{a}{2} (2n - 1)}}}$

Hope this helps :D

Answer 2

Given :-

• Mass Of Hammer = 500g = 0.5kg

• Final Velocity = 50 m/s.

• Initial Velocity = 0 m/s.

• Time = 0.01 seconds.

To Find :-

• Force Of the Nail On The Hammer.

Solution :-

First, We will calculate Acceleration.

Formula Used :-

v = u + at.

Put the values.

➙ 50 = 0 + 0.01a

➙ 0.01a = 50

➙ a = -50/0.01

➙ a = -5000m/s²

Now, Calculating Force.

We know that,

F = ma.

➙ F = 0.5 × -5000

➙ F = 2500 N.

Therefore, Force = 2500 Newton.