Answer to Question #194300 in Math for Sarah

Question

A piece of lead falls from a height of 100 meters on a fixed non _ conducting slad which brings it to rest. Show that it is temperature immediately 7.5°c, knowing that the specific heat of lead is 0.13 J/g°c.)

Answer 1

When the lead ball falls on the non-conducting surface, the lost potential energy is absorbed by the ball as heat energy.

Potential energy of lead $=$ thermal energy of slab

$$mgh=Cm\varDelta T$$

$$\varDelta T=\dfrac{gh}{C}$$

Given $g=9.8\ m/s^{2}, h=100\ m,$

$C=0.13\ J/(g \degree C)=130\ J/(kg \degree C)$

Substitute

$$\varDelta T=\dfrac{9.8\ m/s^{2}\cdot100\ m}{130\ J/(kg \degree C)}=\dfrac{98}{13}\ \degree C$$

$$\varDelta T=7.5\ \degree C$$