Halliday, Resnick & Walker — Center of Mass and Linear Momentum: Problem 15

15 Figure 9-34 shows an arrangement with an air track, in which a cart is connected by a cord to a hanging block. The cart has mass \(m_1 = 0.600 \text{ kg}\), and its center is initially at xy coordinates \(( -0.500 \text{ m}, 0 \text{ m} )\); the block has mass \(m_2 = 0.400 \text{ kg}\), and its center is initially at xy coordinates \(( 0, -0.100 \text{ m} )\). The mass of the cord and pulley are negligible. The cart is released from rest, and both cart and block move until the cart hits the pulley. The friction between the cart and the air track and between the pulley and its axle is negligible. (a) In unit-vector notation, what is the acceleration of the center of mass of the cart–block system? (b) What is the velocity of the com as a function of time \(t\)? (c) Sketch the path taken by the com. (d) If the path is curved, determine whether it bulges upward to the right or downward to the left, and if it is straight, find the angle between it and the x axis.