A train consists of an engine of mass 5000 kg pulling two cars of masses 2000 kg and 3000 kg in a straight line on a horizontal track. The train accelerates at 2 m/s². What is the tension in the coupling between the two cars behind the engine?
Two blocks of masses 6 kg and 4 kg are connected by a light inextensible string over a smooth pulley. The 6 kg block is on a smooth horizontal table, and the 4 kg block hangs freely. What is the tension in the string when the system is released?
Block A of mass 6 kg rests on a rough 30° incline and is connected over a smooth pulley at the top to a hanging block B of mass 5 kg. The coefficient of kinetic friction between block A and the plane is 0.10. Friction is calculated by multiplying the kinetic friction coefficient with the normal force. When released, the system moves with block B descending. Taking g = 10 m/s², what is the magnitude of the acceleration of the system?
An elevator of mass 800 kg is connected over a frictionless pulley to a counterweight of mass 600 kg. The system is released from rest. Taking g = 10 m/s², what is the tension in the cable?
A satellite orbits Planet X at a constant speed in a circular path. The gravitational force provides the centripetal force needed for the orbit. The orbital speed v is related to the planet's mass M and orbital radius r by the formula v = √(G M / r), where G is the gravitational constant. If the mass of Planet X is doubled, while the orbital radius of the satellite remains the same, how must the orbital speed of the satellite change to maintain a stable orbit?