91影视

Mass of the car:$m_1=1000\text{kg}$

Mass of the truck:$m_2=3000\text{kg}$

Initial velocity of the car:$v_1=30\text{m}/\text{s}$

Initial velocity of the truck:$v_2=-20\text{m}/\text{s}$

If the total system kinetic energy before the collision equals the energy after the collision, then it is an elastic collision and If the total kinetic energy is not conserved then it is referred to as an inelastic collision.

All vectors in this system are 1-dimensional, in the x direction.

The velocity of the centre of momentum system of two particles:

$$\begin{gathered} v_{CM}=\frac{m_1{v}_1+m_2{v}_2}{m_1+m_2} \\ {v}_{CM}=\frac{(1000脳30)+(3000脳-20)}{4000} \\ {v}_{CM}=-7.5\text{m}/\text{s} \end{gathered}$$

We find the relative velocities of the car and the truck by subtracting the centre-of-momentum velocity from the original velocities, so the relative velocity of the car:

$v_{1,rel}=v_1-v_{CM}=30-(-7.5)=37.5\text{m}/\text{s}$

And the relative velocity of the truck:

$v_{2,rel}=v_2-v_{CM}=-20-(-7.5)=-12.5\text{m}/\text{s}$

So, the total initial kinetic energy in the CM frame:

$\begin{array}{rcl}K{E}_{rel,i}& =& K{E}_{{\text{rel}}_l,1}+K{E}_{\text{rel}/2}\\ & =& \frac{1}{2}{m}_1{v}_{\text{rel},1}^2+\frac{1}{2}{m}_2{v}_{rel,2}^2\end{array}$

$$\begin{gathered} K{E}_{\text{rel,i}}=\left(\frac{1}{2}脳1000脳{(37.5)}^2\right)+\left(\frac{1}{2}脳3000脳{(-12.5)}^2\right) \\ K{E}_{\text{rel,i}}=9.4脳{10}^5\text{J} \end{gathered}$$

The vehicles stick together, so in the CM frame $K{E}_{rel,f}=0$and the change in kinetic energy:

$\begin{array}{rcl}螖KE& =& K{E}_{\text{rel},f}-K{E}_{\text{rel},i}\\ & =& -K{E}_{\text{rcl},i}\end{array}$

$螖KE=-9.4脳{10}^5\text{J}$