Physics incline vs curve ramp.

[JohnDoe12]

Identical blocks released at same height above a tabletop onto a curved and incline ramp side by side. How will their speeds compare when they reach the tabletop? How will their time of arrival at the tabletop compare? One is an incline, one is a curve so I assume the curved ramp will have a greater acceleration?

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[jetsfan1234]

The blocks will have the same final speed due to the principle of energy conservation. Initial potential energy = final kinetic energy.

When you say "curved ramp" do you mean like a winding ramp? If so, the time on the curved ramp will be longer, since distance traveled is greater. Acceleration would be lower than on the straight ramp.

 

[JohnDoe12]

Not winding. Just curved. Like a vert ramp. The other is a simple incline but both have same heights.

 

[CarefreeSurfboard]

Identical blocks released at same height above a tabletop onto a curved and incline ramp side by side. How will their speeds compare when they reach the tabletop? How will their time of arrival at the tabletop compare? One is an incline, one is a curve so I assume the curved ramp will have a greater acceleration?

http://i.imgur.com/nxavhIw.jpg

I hope this helps. Let me know if there are any errors.

Also just as a clarification:
Gravity is a conservative force annnnd

Taken from: http://hyperphysics.phy-astr.gsu.edu/hbase/pegrav.html

 

[sazerac]

If it is curved so that the block can gain some vertical distance early on, then it will arrive at the destination with the same final speed but at an earlier time. Galileo thought a circle was the fastest path (and he proved that it was faster than following any number of chords) but a Bernoulli brother later proved that the fastest path shape is actually a cycloid.

Look in Wikipedia for "cycloid" or "brachistochrone curve" for more info.