Conservation of Momentum of two carts Problem

[eraemia]

Homework Statement

Two carts, each with a mass of 1kg, are moving along a track towards one another. One cart is moving to the right at 4m/s and the other is moving to the left at 2m/s. Write down the momentum vector for each cart in column vector notation. Add these together to get the total momentum vector for the system of carts. Assuming this is conserved in the impending collision, and that the cart initially moving to the right ends up at rest after the collision, find the final velocity of the second cart in column vector notation.

Homework Equations

The Attempt at a Solution

ma = 1kg
vaix = 4m/s
vafx = 0 m/s

mb = 1kg
vbix = -2m/s
vbfx = ?

ma*vai + mb*vbix = ma*vafx + mb*vbfx

(1 kg)([4,0,0]m/s) + (1kg)([-2,0,0]m/s) = (1kg)([0,0,0]m/s) + (1kg)(vbfx)

vbfx = [2,0,0] m/s (is this correct column vector notation?)

 

[neutrino]

That's a row-vector, actually. Column vectors are either witten as the transpose of a row-vector
[2,0,0]^T, which is convenient if you want it to fit in a line. Or it can also written as

$$\left[\begin{array}{cc}2\\0\\0\end{array}\right]$$

 

[m2003]

Yes, your solution is correct. In this problem, the conservation of momentum principle states that the total momentum of the system before the collision is equal to the total momentum after the collision. By setting up the equation and solving for the final velocity of the second cart, you have correctly applied the conservation of momentum principle. Your solution is also in the correct column vector notation, as each vector is represented by its x, y, and z components. Well done!