Question

A cart with mass m1 = 3.2 kg and initial velocity of v1,i = 2.1 m/s collides with another cart of mass M2 = 4.3 kg which is initially at rest in the lab frame. The collision is completely elastic, and the wheels on the carts can be treated as massless and frictionless. What is the velocity of m1 in the center of mass frame after the collision?

Answer 1

Answer:

-1.204 m/s

Explanation:

$m_1$ = Mass of first cart = 3.2 kg

$m_2$ = Mass of second cart = 4.3 kg

$u_1$ = Initial Velocity of first cart = 2.1 m/s

$u_2$ = Initial Velocity of second cart = 0 m/s

$v_c$ = Velocity of center of mass

For elastic collision

$m_1u_1 + m_2u_2 =(m_1 + m_2)v_c\\\Rightarrow v_c=\frac{m_1u_1 + m_2u_2}{m_1 + m_2}\\\Rightarrow v_c=\frac{3.2\times 2.1 + 4.3\times 0}{3.2 + 4.3}\\\Rightarrow v_c=0.896\ m/s$

Velocity of $m_1$

$V_m_1=2.1-0.896=1.204\ m/s$

When considering the center of mass frame $V_m_1=-1.204\ m/s$