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Suppose the stick slides without friction along flat surface. enter image description here

Why in this case N does not do any work? As i see stick not only slides in horizontal direction, but also falls in vertical direction, at least its COM falls.

EDIT: I confused by fact that object actually moves in N's direction. Its COM falls vertically.

Yola
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2 Answers2

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The normal/support force doesn't do work in most cases, as work requires force through a displacement in the same direction as the force. However, it does affect the momentum of the object which only requires force over a period of time.

The work from the gravity force becomes linear and rotational kinetic energy. The change in momentum required to turn some of the linear movement into rotational movement came from the Normal force.

Richard
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  • Sorry what do you mean with force through a displacement? – Yola Jan 12 '15 at 10:53
  • @Yola Work = force x distance. The force needs to act on the object as it moves in the direction of the force. If the object does not move, its energy does not change. If it moves against the force, the object is losing energy. If it is moving perpendicular to the force, it also does not affect the energy of the object. If it is moving with the force, in the direction of the force, it is gaining energy due to the force. The force is working on the object. – Richard Jan 12 '15 at 10:59
  • But at the picture we clearly see that stick moves in N's direction. This is the point in the question. – Yola Jan 12 '15 at 11:08
  • There are always multiple ways of analysing a situation, and problems are often solved by creating multiple equations from different pictures of the same problem. In this particular picture it is easier to think of it as two point objects tethered together. The point object that the normal force is acting on does not actually move parallel to the force, hence the force does no work in this picture. – Richard Jan 12 '15 at 11:19
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Work is defined as $$W =\int F \cdot dx= \int F \cos {\theta}dx$$ This definition only holds for non rotating objects. When normal force is applied to the object sliding down, the displacement of the object occurs along the incline. So the angle between force applied and displacement is 90°.

Your question is explained because the work done is not because the object does not slide along the plane. You would also have to use concepts of rotational mechanics to calculate work. In rotational mechanics, $$ W = \int \tau d\theta +\int F \cdot dx$$ Where $\tau$ is torque about the axis through centre of mass. The work done by normal no longer zero as it generated torque.

Incidentally, the work fine would be zero if the object were to slide down a curved path as long as it slid along it.

praeseo
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