Question

A 310-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

Answer 1

The speed of the center of mass of the two carts is 0.049 m/s.

Step-by-step explanation:

Given;

mass of the first cart, m₁ = 310 g = 0.31 kg

speed of the first cart, v₁ = 1.25 m/s

mass of the second cart, m₂ = 270 g = 0.27 kg

speed of the second cart, v₂ = - 1.33 m/s (in opposite direction)

The speed of the center of mass of the two carts is calculated as;

`v_(CM) = (m_1v_1 \ + \ m_2v_2)/(m_1 \ + \ m_2)\\\\ v_(CM) = ((0.31 * 1.25) \ + \ (0.27 * -1.33))/(0.31 \ + \ 0.27) \\\\v_(CM) = (0.3875 \ - \ 0.3591)/(0.58) \\\\ v_(CM) = (0.0284)/(0.58) \\\\v_(CM) = 0.049 \ m/s`

Therefore, the speed of the center of mass of the two carts is 0.049 m/s.