Respuesta :
Answer:
The temperature rise is [tex]143.9\ K[/tex].
Explanation:
Given the mass of the hammer [tex](m)[/tex] is 1.19 kg.
And the speed of the hammer [tex](v)[/tex] is 8.4 m/s.
We need to find the temperature change of iron nail having 20 hammer blows.
First, we will find the kinetic energy of the each blow of hammer.
[tex]K.E=\frac{1}{2}mv^2[/tex]
[tex]K.E=\frac{1}{2}\times 1.19\times 8.4^2=41.99\ J[/tex]
For 20 such blows, the kinetic energy will be
[tex]20\times K.E=20\times 41.99=839.8\ J[/tex]
Let us assume that the nail absorbs all the kinetic energy. So, this 839.8 J will be converted into heat energy [tex](Q)[/tex].
Now,
[tex]Q=839.8\ J[/tex]
Also, we know that
[tex]Q=mc\Delta_T[/tex]
Where,
[tex]m[/tex] is the mass of the nail, which is [tex]13\ g=\frac{13}{1000}=0.013\ kg[/tex]
[tex]c[/tex] is the specific heat capacity of iron, which is 449 J/kg.K
[tex]\Delta_T[/tex] is the change in temperature.
Plug these value we get,
[tex]Q=mc\Delta_T\\839.8\ J=(0.013\ kg)(449\ J/kg.K)\times\Delta_T\\\Delta_T=\frac{839.8}{0.013\times 449}\\\\\Delta_T=143.9\ K[/tex]
We can see the temperature rise is 143.9 K.
