Consider a system of particles in motion $($for example, a pressurized container of gas, where the gas molecules

could be thought of as particles$).$ Suppose the system has $N$ particles, each with mass $m_i$ and velocity

$v_i=v_{x,i}i+v_{y,i}j+v_{z,i}k$ for $i=1,2,$dots,$N$ at some particular moment in time. The total momentum of this

system can be computed as

$p={\displaystyle \underset{i=1}{\overset{N}{}}}{m}_i{v}_i$

and the total kinetic energy of the system could be computed as

$E=\frac{1}{2}{\displaystyle \underset{i=1}{\overset{N}{}}}{m}_i|v_i{|}^2$

where $|v_i|=\sqrt[\phantom{2}]{v_{x,i}^2+v_{y,i}^2+v_{z,i}^2}$ denotes the magnitude $($vector norm$)$ of the velocity of particle $i.$

Write a function calc$\_$mom$\_$energy $(m,v)$ that computes and returns the total momentum $p$ and kinetic energy $E$

of the system. The input $m$ is a $1$D numpy array of size $N$ that contains a list of particle masses, and the input $v$

is a $N32$D numpy array, where each row contains the velocity components $(v_{x,i},v_{y,i},v_{z,i})$ of particle $i.$

Additionally, your code should perform basic error checking on the validity of the inputs by returning $p=$

$np*zeros(3)$ for momentum and $E=$ for the kinetic energy if either of the following is true:

The length of $m$ and the number of rows in $v$ are not equal

$v$ does not have $3$ columns

In your code below, the following function will be graded by checking several sets of input arguments: