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Re: [Phys-l] time to bottom of ramp



I'm having trouble picturing the arc, but if it is shaped such that there is a steeper drop in height early in the travel, then the block traveling the arc could arrive at the "end" sooner as it will have gained speed earlier and traveled at the higher speed for a longer distance than the block sliding down the incline.
Pati

fizix29@aol.com wrote:

From Tipler, 5th ed., problem 7-8:

"You are given two frictionless ramps and a block to slide down them. One ramp is in the form of an inclined plane with height H and length L. The other ramp is cut in the form of a partial arc of a circle, but also has height H and length L. (my note: according to the diagram in the problem what they mean by length L is the horizontal length of the ramp, not the arc length. Also the circular ramp has a horizontal section; it looks like a capital J lying on its side.) You slide the block down each ramp, starting from rest, and measure the time it takes to reach the bottom (my note: I assume they mean "the end of the ramp" since the mass will reach the bottom of the circular ramp before it reaches the end of the ramp) and the speed of the block upon getting there. You find that..."

Answer provided by the publisher:

"Because the block sliding down the circular arc travels a greater distance (an arc length is greater than the length of the chord it defines) but arrives at the bottom of the ramp with the same speed that it had at the bottom of the inclined plane, it will require more time to arrive at the bottom of the arc. "

I disagree.

Comments?

Justin Parke
Oakland Mills High School
Columbia, MD


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