91影视

A property of a moving body that a body has by virtue of its mass and motion, which is equal to the product of the body's mass and velocity.

A fundamental law of physics and chemistry states that the total energy of an isolated system is constant despite internal changes.

As the collision is completely inelastic, kinetic energy will be lost, and the internal energy to increase.

Consider the known data as below.

The relativistic factors is ${纬}_{0.6c}=\frac{5}{4}$and ${纬}_{0.8c}=\frac{5}{3}$.

To determine m₂ in this case of completely inelastic collision let鈥檚 apply momentum conservation as below.

$$\begin{gathered} {纬}_1{m}_1{u}_1+{纬}_2{m}_2{u}_2={纬}_f{m}_f{u}_f \\ {纬}_{0.8c}{m}_1\left(0.8c\right)+{纬}_{0.6c}{m}_2\left(-0.6c\right)=0 \\ \left(\frac{5}{3}\right)\left(0.8\right)m_1=\left(\frac{5}{4}\right)\left(0.6\right)m_2 \\ {m}_2=\frac{16}{3}{m}_1 \end{gathered}$$

Now applying relativistic kinetic energy conservation equation,

$\begin{array}{rcl}螖KE& =& \left[\left({纬}_0-1\right)m_f{c}^2\right]-\left[\left({纬}_{0.8c}-1\right)m_1{c}^2+\left({纬}_{0.6c}-1\right)m_2{c}^2\right]\\ & =& 0-\left[\left(\frac{5}{3}-1\right)m_1+\left(\frac{5}{4}-1\right)m_2\right]c^2\\ & =& -\left[\frac{2}{3}{m}_1+\frac{1}{4}\left(\frac{16}{3}{m}_1\right)\right]c^2\\ & =& -2m_1{c}^2\end{array}$

The change in relativistic kinetic energy will result in change in Internal energy which implies that mass will change.

In this case, the mass will increase because kinetic energy decreases.

$螖KE=-螖m{c}^2$

Put this term in above result, and you get,

$$\begin{gathered} -螖m{c}^2=-2m_1{c}^2 \\ \left[m_f-\left(m_1+m_2\right)\right]=2m_1 \\ \left[m_f-m_1-\left(\frac{16}{3}{m}_1\right)\right]=2m_1 \end{gathered}$$

$\begin{array}{rcl}3m_f-3m_1-16m_1& =& 6m_1\\ 3m_f& =& 25m_1\\ m_f& =& \frac{25}{3}{m}_1\end{array}$

Hence, there is an increase in mass by 2m₁of the system which is a result of decrease in the kinetic energy by 2m₁c² of the system.