Assume you are given two objects whose centre of mass is located exactly at the origin. The first object has a mass of 33 kg and is located at position +30 m with respect to the origin. If the mass of the second object is 7.0 kg, what is its position (in m) with respect to the origin? (Include the sign if the answer is negative, and no sign if the answer is positive.)
To find the position of the second object with respect to the origin, we need to use the concept of the center of mass. The center of mass of a system is the weighted average of the positions of all the masses in the system, based on their respective masses.
In this case, the center of mass of the two objects is located at the origin. This means that the total mass of the system is equal to the sum of the individual masses and their positions must balance out the system.
Let's denote the position of the second object as x (in meters). We can set up an equation based on the center of mass:
(33 kg * 30 m + 7 kg * x) / (33 kg + 7 kg) = 0
Simplifying the equation, we have:
(990 kg*m + 7 kg * x) / 40 kg = 0
Multiplying both sides by 40 kg:
990 kg*m + 7 kg * x = 0
Subtracting 990 kg*m from both sides:
7 kg * x = -990 kg*m
Dividing both sides by 7 kg:
x = -990 kg*m / 7 kg
Evaluating the expression, we find:
x = -141.43 m
Therefore, the position of the second object with respect to the origin is -141.43 meters.