A 67 kg astronaut (Jeff), an 88 kg astronaut (Brett) and a 17 kg rock are tied together by a light rope during a space walk. The distance between Jeff and the rock is 5.0 m, the distance between Brett and the rock is 2.0 m.
Find the position of the centre of mass of the system (measured from Jeff).
To find the position of the center of mass of the system, we need to calculate the weighted average of the positions of each object.
First, we need to determine the total mass of the system by summing up the individual masses of Jeff, Brett, and the rock:
Total mass = mass of Jeff + mass of Brett + mass of rock
Total mass = 67 kg + 88 kg + 17 kg
Total mass = 172 kg
Next, we can calculate the weighted average using the formula:
Position of center of mass = (mass of Jeff * position of Jeff + mass of Brett * position of Brett + mass of rock * position of rock) / Total mass
Let's plug in the given values:
Position of center of mass = (67 kg * 5.0 m + 88 kg * 2.0 m + 17 kg * 0 m) / 172 kg
Position of center of mass = (335 kg*m + 176 kg*m) / 172 kg
Position of center of mass = 511 kg*m / 172 kg
Position of center of mass = 2.97 m
Therefore, the position of the center of mass of the system, measured from Jeff, is approximately 2.97 meters.