1)
The momentum is defined as:
[tex]p=mv[/tex]where m is the mass of the object and v is its velocity.
Let us denote the car from the left as car L and the car from the right as car R; also let us assume that the postive direction is to the right and the negative direction is to the left.
The momentun of the car on the left is:
[tex]p_L=(860)(18)=15480[/tex]The momentum of the car on the right is:
[tex]p_R=(840)(-24)=-20160[/tex]To determine the total momentum of the system we need to add the momentum of each car, then:
[tex]p_L+p_R=15480-20160=-4680[/tex]Therefore the total momentum is -4680 m*kg/s
2)
In a collision the total momentum is conserved, this means that the momentum before the collision is the same as the momentum after it. This can be express as:
[tex]p_i=p_f[/tex]From the previous point we know the initial momentum; ans we know that after the collision the cars stick together, this means that the final momentum is given by:
[tex]p_f=(m_L+m_R)v[/tex]then we have:
[tex]\begin{gathered} -4680=(860+840)v \\ v=-\frac{4680}{860+840} \\ v=-2.75 \end{gathered}[/tex]Therefore, the velocity of the cars after the collision is -2.75 m/s (The minus sign indicate that the cars move to the left after the collision.)
3)
The kinetic energy is defined as:
[tex]K=\frac{1}{2}mv^2[/tex]The total initial kinetic energy is:
[tex]\begin{gathered} K_i=\frac{1}{2}(860)(18)^2+\frac{1}{2}(840)(-24)^2 \\ K_i=381240 \end{gathered}[/tex]The total final kinetic energy is:
[tex]\begin{gathered} K_f=\frac{1}{2}(860+840)(-2.75) \\ K_f=6428.125_{} \end{gathered}[/tex]The change in kinetic energy is:
[tex]\begin{gathered} \Delta K=K_f-K_i_{} \\ \Delta K=6428.125-381240 \\ \Delta K=-374811.875 \end{gathered}[/tex]Therefore, the change in kinetic energy is -374811.875 J (The minus sign idicates that the system lost energy in the collision)
