A 45 kg woman stands up on a 60 kg platform of length 5m, that sits on a frictionless surface. She walks from a point 1 meter from one end of the platform to a point 1 meter from the other end of the platform. Assume the walking velocity vwalk of the woman is variable!! Calculate how far the canoe (platform) slides during the walk.
we know that in the absense of a net external force the velocity of an object remains constant or remains zero if it was initially in rest.since the platform was initially at rest,it will not move and as a result centre of mass will not move
now equation of centre of mass is
now i am taking origin at centre of platform .SO
earlier centre of mass was at (60 x0 + 45 x 1.5)/105=0.643m from centre of platform towards first end (say right side) of platform
now let movement of platform be x m from its centre towards right side when lady moves towards left side.
therefore 0.643=(60* x +45 * (-1.5+x))/105
therefore x =1.2857 m towards the first end(right side) of platform