Question

A 310-g air track cart is traveling at 1.25 m/s and a 260-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 310-g air track cart is traveling at 1.25 m/s and a 260-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? 1.47 m/s 0.131 m/s 2.80 m/s 1.29 m/s 0.0732 m/s

Answer 1

Answer:

$v_{CM}=0.0732\ m/s$

Explanation:

given,

mass of the cart 1, m₁ = 310 g

speed of car 1 , v₁ = 1.25 m/s

mass of cart 2, m₂ = 260 g

speed of cart 2, v₂ = -1.33 m/s

speed of center of mass

$v_{CM}=\dfrac{m_1v_1 + m_2 v_2}{m_1 + m_2}$

$v_{CM}=\dfrac{0.31\times 1.25 +0.26\times (-1.33)}{0.31+0.26}$

$v_{CM}=\dfrac{0.0417}{0.57}$

$v_{CM}=0.0732\ m/s$

Hence, speed of center of mass of the system is equal to 0.0732 m/s

Answer 2

The speed of center of mass of the carts system is 0.073 m/s.

The given parameters:

• Mass of the cart 1, m₁ = 310 g = 0.31 kg
• Speed of car 1 , v₁ = 1.25 m/s
• Mass of cart 2, m₂ = 260 g = 2.6 kg
• Speed of cart 2, v₂ = -1.33 m/s

The speed of center of mass of the carts system is calculated as follows;

$V_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} \\\\V_{cm} = \frac{0.31 \times 1.25 \ + \ 0.26 (-1.33)}{0.31 + 0.26} \\\\V_{cm} = 0.073 \ m/s$

Thus, the speed of center of mass of the carts system is 0.073 m/s.

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