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Take for example a slide of 3m tall.

Would an object (starting from rest) sliding down a gentle slope have a lower speed than a steep slope? (Note: Height of slide is the same,disregard friction.)

Why is this so?

What if the slide was a spiral one?

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I guess your question is about the final speed (at the bottom of the slide) of a body that started to move down the slide with the initial speed (at the top of the slide) equal to zero. If you disregard friction (and air resistance), the final speed will depend on the height of the slide only, not on its slope (or the shape - straight or spiral). However, the body will get to the bottom of the slide faster when the slide slope is greater.

Note that you should compare speeds (which are scalars), rather than velocities (which are vectors).

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  • $\begingroup$ but why is this so though? $\endgroup$ – user81675 Aug 31 '13 at 16:04
  • $\begingroup$ Because, if there is no friction, mechanical energy is conserved. Mechanical energy is the sum of potential energy and kinetic energy. In your case, potential energy depends on the mass and the height only, kinetic energy depends on the mass and the speed only. If you wonder why mechanical energy is conserved... Well, that follows from the Newton's laws. Why should we accept the Newton's laws? Based on results of experiments... $\endgroup$ – akhmeteli Aug 31 '13 at 16:09
  • $\begingroup$ Yes, based on the Principle of Conservation of Mechanical Energy, the speed at which the object would travel would be the same, regardless of whether it is placed on a steep slope or on a gentle slope. What I'm asking is, why would an object travel at a greater speed when placed on a steep slope? Doesn't it have to do with gravity? $\endgroup$ – user81675 Aug 31 '13 at 16:20
  • $\begingroup$ If you disregard friction, the final speed will be the same, no matter what slope. If you wonder why a body reaches this speed faster on a steeper slope... Well, that follows from the Newton's laws. $\endgroup$ – akhmeteli Aug 31 '13 at 16:25

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