Answer to Question #85253 in Mechanics | Relativity for Murari

Question

When we push a book on table and leave it travels a distance and stops due to friction
But I want to know that when we slide the book on table by constantly keeping our hand over it then we suddenly stop sliding then at that instant the book stops, so does that mean that friction.is the reason or the force which we were applying has become zero and has stopped its motion?

Answer 1

When we push a book on table and leave, it has initial velocity and it will travel by inertia until its velocity becomes equal to 0 due to the friction:

F_fr=ma=m (ϑ-ϑ_0)/t=-m ϑ_0/t

This initial velocity book has because the force implied to the book by us was bigger than the friction force.

F-F_fr=ma^'

ϑ^'=ϑ_0^'+a^' t^'=a^' t^'

But when we slide the book on table by constantly keeping our hand over it the force implied to the book by us is equal to the friction force (book is moving with constant velocity):

F-F_fr=0,

a=0,

ϑ=const

After you stop pushing it stops immediately since there is no reason to move.

Answer: The reason of stopping is both the presence of friction force and the absence of applied force. Book was moving because of the applied force, that was equal to the friction force. When you take your hand, there is only friction force and no applied force (no reason to move).