Given :- Mass of Hammer = 1 kg
- Mass of Iron Nail = 0.2 kg (200g)
- Velocity of Hammer = 50m/s
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