Before coming to my actual question, let me write some assumptions that I believe we both agree on:-(1) Normal force can do work(for example in an elevator)(2) Normal force is always perpendicular to the contact area. questions says
My doubt arises in part(b)The general solution for this part that I have found everywhere is using energy conservation. It is said that the kinetic energy of ‘m’ initially is equal to the kinetic of it at the highest point+the kinetic energy of ‘M’+mgh.
But I object to it. My argument is that the normal force is also doing work here and so we cannot use work energy conservation.Let us consider the object m at some point A.
As I have written, this force must lead to a velocity of M parallel to ground. Hence we can say M has some velocity parallel to ground.m has velocity parallel to the contact area relative to M. thus we can say in the frame of M,
And this relative velocity will be perpendicular to the normal force exerted on m.We know that velocity of m wrt ground = velocity of m wrt M + velocity of M wrt ground.Velocity of m wrt M is parallel to the contact and velocity of M wrt ground is parallel to ground. Hence velocity of m wrt ground will look something like
And so this velocity will NOT make a 90degree angle with the normal force. Similarly the displacement vector of m will NOT make a 90 degree angle with normal force..
So net displacement of m will not be perpendicular to the normal force.
Hence we can conclude that normal force in the curved path would do some work.So we cannot use conservation of energy in inertial frame.But if we don’t use that then we won’t get the right answer.What is the fault in my reasoning?
