A 1.0 kg hammer with a velocity of 50 m/s strikes a 200 g iron nail driving it into a block of wood. If half of the energy of the hammer goes into heating the nail, what will be rise in its temeperature? (Specific heat capacity of iron = 419J/kg°C) REQUEST = SPAM N KARE _/\_ THANKS! HOPING FOR A GREAT ANSWER _/\_

Answers 2

Explanation:

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Given :

To Find :

Rise (or change) in the temperature if the Hammer uses half of its energy in heating the nail

Solution :

First, Let's Find out the initial energy of the Hammer:

[tex] \implies \displaystyle \rm ke = \frac{1}{2} m {v}^{2} [/tex]

[tex] \implies \displaystyle \rm ke = \frac{1}{2} {50}^{2} [/tex]

[tex] \implies \displaystyle \rm ke = \frac{1}{2} {2500}[/tex]

[tex] \implies \displaystyle \rm ke = {1250}j[/tex]

So, The initial Energy of Hammer = 1250 J

As Given, Half of the energy is used in Heating up the Iron nail,

So, Q = Initial Energy/2

or, Q = 1250/2

or, Q = 625

So, The heat energy produced is 625J

Now, using the Formula :

[tex] \implies \displaystyle \rm q = mc \triangle t[/tex]

[tex] \implies \displaystyle \rm 625= 0.2 \times 419 \times \triangle t[/tex]

[tex] \implies \displaystyle \rm 3125= 419 \times \triangle t[/tex]

[tex] \implies \displaystyle \rm\triangle t = \frac{3125}{419} [/tex]

[tex] \implies \displaystyle \rm\triangle t = 7.4[/tex]

So, the Change in Temperature = 7.4°C