Question

A spring pushes against two horizontal carts that are held together by a thread on a frictionless surface. Cart A is 1.5-kg and Cart B is 4.5-kg. The thread is then burned, releasing the stored energy of the spring and the carts move away from each other. The Cart A moves with a velocity of 27 cm/s to the left. What is the velocity of the Cart B, in cm/s?

Answer 1

Given:

The mass of car A is

`m_A=1.5\text{ kg}`

The mass of car B is,

`m_B=4.5\text{ kg}`

The speed of car A is

`\begin{gathered} v_A=27\text{ cm/s} \\ =0.27\text{ m/s} \end{gathered}`

to the left

To find:

The velocity of car B in cm/s

Step-by-step explanation:

Before the thread is burned, the total momentum of the two carts is zero, as nothing moves. So, after the thread releases the carts, the total momentum must still be zero as per the conservation of linear momentum.

So, we write,

`\begin{gathered} m_Av_A+m_Bv_B=0 \\ v_B=-(m_Av_A)/(m_B) \\ v_B=-(1.5*27)/(4.5) \\ v_B=-9\text{ cm/s} \end{gathered}`

Hence, the cart B goes in the opposite direction at a speed of 9 cm/s