Johns mass is 85.4 kg, and Barbars is 55.2 kg. He is standing on the x axis at xJ = +9.01 m, while she is standing on the x axis at xB = +4.65 m. They switch positions. How far and in which direction does their center of mass move as a result of the switch?
the distance between them is constant, but the cm will be closer to the larger mass
separation ... 9.01 - 4.65 = 4.36 m
cm ... 85.4 d = 55.2 (4.36 - d)
... d is the distance from John
when they switch, the cm will be closer to the origin
... because John will be closer to the origin
To determine how far and in which direction the center of mass moves as a result of John and Barbara switching positions, we can calculate the coordinates of the new center of mass using the following formula:
x_cm = (mJ * xJ + mB * xB) / (mJ + mB)
Where:
- x_cm is the x-coordinate of the center of mass
- mJ is John's mass
- xJ is John's initial position
- mB is Barbara's mass
- xB is Barbara's initial position
Plugging in the values:
x_cm = (85.4 kg * 9.01 m + 55.2 kg * 4.65 m) / (85.4 kg + 55.2 kg)
x_cm = (769.554 kg·m + 256.368 kg·m) / 140.6 kg
x_cm = 1025.922 kg·m / 140.6 kg
x_cm ≈ 7.29 m
Therefore, the center of mass moves approximately 7.29 meters to the left (in the negative x-direction) as a result of John and Barbara switching positions.