Chapter 12, Problem 76A

To determine

To Calculate: The speed of copper blocks before the collision.

Answer to Problem 76A

  $8.8\text{m/s}$

Explanation of Solution

Given:

Mass of copper blocks, $m=0.35\text{kg}$

Initial speed of two blocks is same but they move towards each other and hence, collide.

Final speed of blocks is zero. $v=0$

Change in temperature of the blocks is $\Delta T=0.20°\text{C}$

All the kinetic energy is converted into thermal energy.

Formula Used:

Thermal energy can be obtained by:

  $Q=mc\Delta T$

Where, m is the mass, c is the specific heat capacity and $\Delta T$ is the difference in temperature.

Kinetic energy can be obtained by:

  $K.E.=\frac{1}{2}m\left(v^2-u^2\right)$

Where, m is the mass, v is the final speed and u is the initial speed.

Calculation:

For thermal equilibrium:

Kinetic energy lost by copper block = thermal energy

Specific heat of copper

  $\begin{array}{l}-2\times \frac{1}{2}m\left(v^2-u^2\right)=mc\Delta T\\ \Rightarrow u^2=385\text{J/kg}°\text{C}\times 0.2°\text{C}\\ \Rightarrow u=8.8\text{m/s}\end{array}$

Conclusion:

Thus, the speed of blocks before collision is $8.8\text{m/s}$ .