Question

6. A steel object was released from rest at a height of 150 m. What will be the change in temperature of the object after it hits the ground? Assume that 80% of the initial mechanical energy was absorbed by the object when it hits the ground. Specific heat of steel is c = 460 (15 points)

Answer 1

Let the mass of the steel is m.

The height from where the object is released is h=150 m.

The specific heat of steel is C=460 J/kg.^oC.

From the conservation of energy, we can say the potential energy changed to mechanical energy and the absorbed mechanical energy to heat energy that increased the temperature.

  $mgh\times \frac{80}{100}=mC\Delta T$

  $or\: \: \: \: \: \: \Delta T=\frac{gh}{C}\times \frac{80}{100}$

$or\: \: \: \: \: \: \Delta T=\frac{9.8\times 150}{460}\times \frac{80}{100}$

$\therefore \: \: \: \: \: \: \Delta T=2.556521739\approx 2.56^{\circ}\: \: C$

$\therefore$ The change in temperature is 2.556521739^oC or 2.56^oC approximately.