A 100 g of iron nail is hit by a 1 . 5 kg hammer striking at a velocity of 60 ms - 1 . What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the

Question

A 100 g of iron nail is hit by a 1 . 5 kg hammer striking at a velocity of 60 ms - 1 . What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail ? [Specific heat capacity of iron = 0 . 42 Jg - 1 C ∘ - 1 ]

TestHub · Accepted Answer

If we heat-up an object, then, the energy is used to either change the temperature of the body or to change the state of the body.
If it changes the temperature, then,

$Q = m S ∆ T$
where, $Q$ is the heat given, $m$ is the mass and $∆ T$ is the change in temperature.

We know that a moving object has an energy in the form of kinetic energy, i.e.,
$K E = \frac{1}{2} m v^{2}$

When that moving object strikes another object, it loses some energy which changes into the heat energy and this heat energy increases the temperature of the object.
Given a hammer of $1.5 kg$ is moving with $60 m s^{- 1}$ .
Kinetic energy $= \frac{1}{2} m v^{2} = \frac{1}{2} (1.5) (60)^{2} = 2700 J$
One-fourth of kinetic energy changes into heat energy.
$\Rightarrow \frac{1}{4} (K E) =$ Heat energy
$\Rightarrow \frac{1}{4} (K E) = m (S) (∆ T)$
$\Rightarrow \frac{1}{4} (2700) = (100) (0.42) (∆ T)$
$\Rightarrow ∆ T = 16.07 ° C$

Physics - Heat & Thermo Question with Solution | TestHub

Options:

Doubts & Discussion