A 320-g air track cart is traveling at 1.25 m/s and a 270-g cart traveling in the opposite direction at 1.33 m/s. What is the speed of the center of mass of the two carts?
A)2.80 m/s
B)0.0693 m/s
C)0.131 m/s
D)1.47 m/s
E)1.29 m/s

Question

Quizplus · Accepted Answer

The speed of the center of mass is given by:$$v_{cm}=\frac{m_1v_1+m_2v_2}{m_1+m_2}$$where $m_1$ and $v_1$ are the mass and velocity of the first cart, and $m_2$ and $v_2$ are the mass and velocity of the second cart.Plugging in the given values, we get:$$v_{cm}=\frac{(0.320	ext{ kg})(1.25	ext{ m/s})+(0.270	ext{ kg})(-1.33	ext{ m/s})}{0.320	ext{ kg}+0.270	ext{ kg}}=0.0693	ext{ m/s}$$Therefore, the speed of the center of mass of the two carts is 0.0693 m/s.

A 320-G Air Track Cart Is Traveling at 1