Question

A 350-g air track cart is traveling at 1.25 m/s and a 280-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

Answer:

The speed of the center of mass of the two carts is 0.103 m/s

Explanation:

It is given that,

Mass of the air track cart, m₁ = 350 g = 0.35 kg

Velocity of air track cart, v₁ = 1.25 m/s

Mass of cart, m₂ = 280 g = 0.28 kg

Velocity of cart, v₂ = -1.33 m/s (it is travelling in opposite direction)

We need to find the speed of the center of mass of the two carts. It is given by the following relation as :

$v_{cm}=\dfrac{m_1v_1+m_2v_2}{m_1+m_2}$

$v_{cm}=\dfrac{0.35\ kg\times 1.25\ m/s+0.28\ kg\times (-1.33\ m/s)}{0.35\ kg+0.28\ kg}$

$v_{cm}=0.103\ m/s$

Hence, this is the required solution.