## BdPhO Regional (Dhaka-South) Secondary 2019/4

Discuss Physics and Physics Olympiad related problems here
SINAN EXPERT
Posts: 38
Joined: Sat Jan 19, 2019 3:35 pm
Location: Dhaka, Bangladesh
Contact:

### BdPhO Regional (Dhaka-South) Secondary 2019/4

Consider an isolated system consisted of a ball, and a bucket of water. The ball is released from height, \$H\$ above a bucket of water. The initial temperature of the water-bucket system and the ball are \$T_1\$ and \$T_2\$ respectively. What will be the final temperature of the water after the ball is dropped? (mass of the ball = \$m_1\$, mass of water = \$m_2\$, mass of the bucket = \$m_3\$, specific heat of ball, water and bucket are \$s_1\$,\$s_2\$ and \$s_3\$ respectively)
\$The\$ \$only\$ \$way\$ \$to\$ \$learn\$ \$mathematics\$ \$is\$ \$to\$ \$do\$ \$mathematics\$. \$-\$ \$PAUL\$ \$HALMOS\$

SINAN EXPERT
Posts: 38
Joined: Sat Jan 19, 2019 3:35 pm
Location: Dhaka, Bangladesh
Contact:

### Re: BdPhO Regional (Dhaka-South) Secondary 2019/4

As the system is isolated, energy cannot enter or get out from it. The ball is released from height, \$H\$. When it touches the ground, the kinetic energy converts into sound and thermal energy. I mean,
\$Kinetic\$ \$Energy\$ \$=\$ \$Sound\$ \$Energy\$ \$+\$ \$Thermal\$ \$Energy\$

But in fact, the sound energy is negligible. So we can say, \$Kinetic\$ \$Energy\$ \$=\$ \$Thermal\$ \$Energy\$

According to the law of calorimetry, LOST HEAT = GAINED HEAT

Let the final temperature of water be \$T\$.

Hence, \$m_1s_1(T_2-T)+m_1gH=(m_2s_2+m_3s_3)(T-T_1)\$

\$∴T=\dfrac{m_1gH+m_1s_1T_2+(m_2s_2+m_3s_3)T_1}{m_1s_1+m_2s_2+m_3s_3}\$
\$The\$ \$only\$ \$way\$ \$to\$ \$learn\$ \$mathematics\$ \$is\$ \$to\$ \$do\$ \$mathematics\$. \$-\$ \$PAUL\$ \$HALMOS\$