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enter image description hereHere in this question , considering the system to be the thread , ladder and man , we can say that as the gravitational force which is and external force equal to 2Mg is acting in the downward direction and the pully exerts an equal and opposite force of 2Mg in the upward direction , hence the center of mass should not move as there is no external force to it as the tension in the thread and force applied by the man on the ladder and the normal force exerted by the ladder on the man as he moves up, are all internal force.

But in the solution the displacement of the center of mass is a non-zero quantity.

enter image description here

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    $\begingroup$ Make a force diagram for the situation with the man climbing. $\endgroup$
    – nasu
    Jun 9, 2022 at 9:45
  • $\begingroup$ Related: physics.stackexchange.com/questions/58193/… $\endgroup$ Jun 9, 2022 at 10:28
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    $\begingroup$ @Steeven The ladder does not touch the floor. It is attached to the rope. $\endgroup$
    – nasu
    Jun 9, 2022 at 13:58
  • $\begingroup$ @nasu Yes i have drawn the force diagram but cannot still figure out what the external force to the system is. $\endgroup$
    – user327809
    Jun 9, 2022 at 14:12
  • $\begingroup$ Where is it? I cnnot see it. $\endgroup$
    – nasu
    Jun 9, 2022 at 17:16

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As far as I understand the man and the ladder both have equal mass. Assuming the man can climb up the ladder without exciting movement in the other mass, the center of mass will shift. This is not a very good assumption since it is said that the pulley is ideal and has no friction, but I see no other way for the COM to shift as the movement is internal to the system.

Note that in the diagram on the right, the length of the rope remain the same, the mass has "climbed" up the rope. Also the COM is a vector quantity, but I have written the y component and didn't bother to write it

This is a simplified version where all the mass climbs up the rope without changing the height of the other mass thereby moving the COM up half the initial height separation.

Your case is a little more complicated since it involves two masses on the right side, one of them climbing up the other is stationary. Again, all of this assuming the ascent of the man doesn't cause the system to move in response which is a questionable assumption at best, but the only one I see which lead to a change to the COM.


  • Note that in the diagram on the right, the length of the rope remains the same, the mass has "climbed" up the rope. Also the COM is a vector quantity, but I have written the y component and didn't bother to write it
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