Recent content by Pratik89

Alright, I have one alternative explanation too, but I am not sure it is correct If the rope extends by x, the centre of mass of the rope should therefore move by x/2. Assuming that the center of mass (of rope) is the point where the new mass is tied, the new mass only moves down by x/2 whereas...

Alright, so this is what you are saying, correct me if I am wrong The mass loses potential energy because it gets lower. This potential energy is distributed to the rope and to the hand equally, because the hand is being acted upon by the mass (weight) of the object

if your claim is that the energy goes to the hand, I am not entirely convinced. Work is defined as force*displacement. The net force on the hand is always zero. So no work has been done on the hand no matter how much it gets displaced

this is exactly what I mention in the second point, the zero to max variation ensures that that sum of forces in point 2 and point 3 adds up to the force in point 1.

The mass is acted upon by these forces 1. It's own weight force 2. At the beginning the rope does not apply any force, and the hand completely supports it. As the mass is lowered, the support required from the hand reduces because the rope takes over. Finally, when the mass is at the lowest...

the hand is not exerting a force, the hand is countering the force because of the force exerted by the mass, the hand initially exerts a force (because we are assuming that the body is always in equilibrium) and this is countered by the force exerted by the mass. As the mass drops, it requires...

it should be positive because the direction of force and motion is the same and I think it would be half of the work done by gravity

It reduces linearly, so the plot of force versus distance would be a dropping line, the energy would be the area under this which is 0.5F*x.

Well, yes the force changes, initially it is equal to the force exerted by the mass of the object, however as it lowers down, the force reduces and finally at equilibrium, the force becomes zero.

The force acting on the hand would be the force due to the mass of the object.

The question does not specify this, but let us assume is it released slowly to the equilibrium position. In either case energy stored in the rope (due to stretching) should be the same

My question is why is it exactly half and where does the other half end up ?

the equilibrium position should be in between the lowest point and the point it was initially released from. So are you saying that, the energy difference is because there is some loss of energy while the mass oscillates ?

It was incorrect, those coordinates belong to the centroid