An astronaut is tethered by a strong cable to a spacecraft. The astronaut and her spacesuit have a total mass of 105 kg, while the mass of the cable is negligible. The mass of the spacecraft is 9.05 × 104 kg. The spacecraft is far from any large astronomical bodies, so we can ignore the gravitational forces on it and the astronaut. We also assume that both the spacecraft and the astronaut are initially at rest in an inertial reference frame. The astronaut then pulls on the cable with a force of 80.0 N. (a) What force does the cable exert on the astronaut? (b) Since how can a “massless” (?m? = 0) cable exert a force? (e) What is the astronaut’s acceleration? (d) What force does the cable exert on the spacecraft? (e) What is the acceleration of the spacecraft?

Solution 44P Step 1: Mass of the astronaut (m) = 105 kg Mass of the cable = 0 Mass of the spacecraft (M) = 9.05 x 10 kg Spacecraft is free from astronomical bodies, there is no gravitational pull Problem (a) Step 1: Force applied by the astronaut = 80N Action = reaction Force exerted on the astronaut = 80N Problem (b) Step 1: Even though the mass of the cable is negligible, the rope can exert force on the astronaut due to tension. Problem (c) Step 1: Astronaut’s acceleration (a ) = m = 105 a = 0.762 m/s 2 Problem (d) Step 1: The force exerted on the spacecraft by the rope. Since the rope is massless, the net force on the rope is negligible and the spacecraft will exert the same force exerted by the rope. That is 80 N. Problem (e) Step 1: Acceleration of the spacecraft = M = 80 4 9.05x10 4 2 = 8.84x10 m/s