Question

Mike's mass is 90 kg, and Helen's mass is 45 kg. Mike stands on the x-axis at 9.0 m and Helen stands on the x-axis at 2.0 m. They switch positions. How far does their center of mass move after the switch?

Answer 1

The center of mass moves 2.34 meters to the left on the x-axis when Mike and Helen switch positions.

Step-by-step explanation:

To determine how far the center of mass moves when Mike and Helen switch positions, we need to calculate the initial and final positions of the center of mass and then find the difference. The center of mass (CM) of a two-particle system can be found using the formula:

CM = (m1*x1 + m2*x2) / (m1 + m2)

Initially, Mike's mass (m1) is 90 kg, and he stands at 9.0 m (x1), while Helen's mass (m2) is 45 kg, and she stands at 2.0 m (x2). So the initial center of mass is:

CM_initial = (90 kg * 9.0 m + 45 kg * 2.0 m) / (90 kg + 45 kg)

CM_initial = (810 kg*m + 90 kg*m) / 135 kg

CM_initial = 900 kg*m / 135 kg

CM_initial = 6.67 m

After they switch positions, the final center of mass is:

CM_final = (90 kg * 2.0 m + 45 kg * 9.0 m) / (90 kg + 45 kg)

CM_final = (180 kg*m + 405 kg*m) / 135 kg

CM_final = 585 kg*m / 135 kg

CM_final = 4.33 m

The center of mass has moved:

CM_movement = CM_final - CM_initial

CM_movement = 4.33 m - 6.67 m

CM_movement = -2.34 m

The negative sign indicates that the center of mass moved to the left on the x-axis.