Meriam, Kraige & Bolton — Kinetics of Systems of Particles: Problem 4_68

4/68 A coil of heavy flexible cable with a total length of 100 m and a mass of 1.2 kg/m is to be laid along a straight horizontal line. The end is secured to a post at A, and the cable peels off the coil and emerges through the horizontal opening in the cart as shown. The cart and drum together have a mass of 40 kg. If the cart is moving to the right with a velocity of 2 m/s when 30 m of cable remain in the drum and the tension in the rope at the post is 2.4 N, determine the force P required to give the cart and drum an acceleration of \(0.3 \text{ m/s}^2\). Neglect all friction.