Confirming an observation about Newton's Laws

[frankfjf]

When approaching a problem concerning Newton's 2nd law of motion, if I'm dealing with a frictionless inclined plane and know the velocity of an object going up the plane, is it safe to say that the velocity will be the same on the way back down since no friction is present?

 

[frankfjf]

This is of course assuming that the object, such as a block, is projected up the plane then allowed to slide back down, and I know the velocity it used to go up the incline.

 

[Doc Al]

is it safe to say that the velocity will be the same on the way back down since no friction is present?

Yes, since mechanical energy is conserved. For the same reason, if you toss a ball upward at some speed, when it falls back down it will have the same speed (ignoring air resistance). (Nitpick: Of course it's the speed that's the same, not the velocity, since the direction of motion is reversed on the way down.)

 

[Chi Meson]

Edit: Darn it DocAl, I was answering this one! Well, this is what I wrote:

Yes (I assume you meant that the final speed at the bottom will be the same as the initial speed as it starts up the incline). Since there is no friction, the only the componant of the weight that is parallel to the surface will act. This means, if the plane is at a constant angle, the acceleration will be a constant g(sin theta), where theta is the angle of incline. Also, from an energy point of view, since no frictional forces are present, mechanical energy is conserved.