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We know that a frictionless plane cannot resist the motion of a body over it...Bit it can apply normal force on the body.

If I stand on such a plane and throw a book forward, I would move backwards. Now, can the frictionless plane apply any impulse of force on me? What would be its direction?

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  • $\begingroup$ What do you mean by 'impulse of force?' $\endgroup$ – Jakob Lovern Jan 9 '18 at 17:27
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    $\begingroup$ The friction-less plane is always applying a normal force on you which is why you don't fall through the plane. If there's no friction, there won't be any force in the horizontal direction. $\endgroup$ – Yashas Jan 9 '18 at 17:45
  • $\begingroup$ I am saying that there is a time required by me to throw the book (suppose t) ...So,there must be an impulse of force,which is force times time or,change of momentum...If I calculate change of momentum,then which direction should I choose? $\endgroup$ – user179960 Jan 9 '18 at 18:06
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    $\begingroup$ What force do you think the plane might apply? If none, why are you asking this question? $\endgroup$ – Bill N Jan 9 '18 at 22:42
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Impulse of force differs from element to element in a system. The momentum of the system as a whole does not change, but the momentum change occurs for every element in the system for the time being...

As you propel the book horizontally during time ∆t, momentum change of that book occurs for the time interval only.In case of the plane,it applies impulse of force only in horizontal direction on the book since there is no component of velocity vertically.So, J=mass of book x Final velocity...

However,I'm confused about the time given.Ican calculate the momentum change for finding impulse of force,then why do I need ∆t?And also what would happen if I throw the book obliquely .Shall I compute impulse of forces for two components of velocity?

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You're standing still holding a book: zero momentum. You throw the book in some direction by applying a force F to it for time t. By Newton's third law, it applies a force -F to you, also for time t. Now it has momentum F t, and you have momentum -F t. The total is still zero, and there was never any horizontal force transmitted by or to the frictionless plane.

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