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Center of Mass : Introduction 0/4
Momentum Conservation & Collision 0/4
Solving Problems using center of mass
Only external force can change the state of motion of Center of mass.
In above diagram, a rod of mass M and length L, is sliding and fall on the ground. Find out the path of Centre of mass of the rod.
Let’s draw free body diagram first,
We can see that only force acting on the rod is in vertical direction. No external force is acting on the rod in horizontal direction. Hence Center of mass of the rod will not move in horizontal direction. So part of Center of mass of rod will be straight line is going through its Center.
Find out the acceleration of Centre of mass of above system. Given that spring is in compressed state.
As there is no external force apart from F is acting on the system. Find calculating acceleration of the Centre of mass we need not consider force applied by spring because it is internal force.
Find out the displacement of plank during the time the man moves distance L on the plank.
In this case there is no external force is acting on the system. Initial velocity of Center of mass of the system is zero. Hence velocity of Center of mass will always be zero in this case. Center of mass of the system will not move even though the man and the plank can move.
We know that man moves a distance L with respect to the plank. Let’s assume that the plank moves X distance in left direction with respect to ground, hence the man will move (L-x) distance in the right direction with respect to ground.
Above system consisting of a balloon and man is in equilibrium and at rest. Find out the displacement of the balloon during the time the man falls on the ground.
It is given that the system is in equilibrium and initial velocity of Centre of mass of the system is zero. As the net external force acting on the system is zero, Centre of mass of the system will not move until net external force acting on the system is zero. That means there will be no displacement of Centre of mass of the system till time the man reaches the ground. As soon as the man reaches the ground system will not be in equilibrium so after that Centre of mass of system will start moving.
Let’s calculate displacement of Centre of mass of system by the time the man just touches the ground, which is equal to 0.
Hence, the balloon will move by mh/M distance in the upward direction by the time man reaches to the ground.