19. Four masses travel towards each other from the four cardinal directions - a $2 m$ mass from the north at speed $v$, an $m$ mass from the South at speed $2 v$, an $m / 2$ mass from the west at $6 v$, and a $3 m$ mass from the east at $v$, as shown. What is the direction of the total momentum of this system?
A. east
B. west
C. northeast
D. The total momentum is zero.
Answer
\(\boxed{\text{D. The total momentum is zero.}}\)
Step 1 ：Given masses and velocities: \(m = 1\), \(v = 1\), \(m_N = 2m\), \(v_N = v\), \(m_S = m\), \(v_S = 2v\), \(m_W = \frac{m}{2}\), \(v_W = 6v\), \(m_E = 3m\), and \(v_E = v\)
Step 2 ：Calculate the momentum in the x-direction: \(p_x = m_Wv_W - m_Ev_E = \frac{1}{2}(6) - 3(1) = 0\)
Step 3 ：Calculate the momentum in the y-direction: \(p_y = m_Nv_N - m_Sv_S = 2(1) - 1(2) = 0\)
Step 4 ：Since both \(p_x\) and \(p_y\) are zero, the total momentum is zero.
Step 5 ：\(\boxed{\text{D. The total momentum is zero.}}\)
