Answer to Question #164017 in Physics for Andu

Question

Two carts with masses respectively m1 = 300g and m2 = 600g are connected to each other by means of a thread and a compressed spring. They move together at a speed of 3m / s. (The thread is elongated, the mass of the thread and the spring is negligible). Once the thread burns and the spring is released, the carts split.

The cart with a mass of m2 moves at a speed of 5m / s. Calculate the speed of the cart with mass m1.

Answer 1

Let's assume that the two carts initially moves to the right and choose rightwards as the positive direction. After the thread burns and the spring is released, the carts split. Let's suppose that the second cart moves to the left after the split. Then, we can apply the law of conservation of linear momentum:

$$(m_1+m_2)v_c=m_1v_1-m_2v_2,$$ $$v_1=\dfrac{(m_1+m_2)v_c+m_2v_2}{m_1},$$ $$v_1=\dfrac{(0.3\ kg+0.6\ kg)\cdot3\ \dfrac{m}{s}+0.6\ kg\cdot5\ \dfrac{m}{s}}{0.3\ kg}=19\ \dfrac{m}{s}.$$

The sign plus means that the velocity of the first cart directed to the right.