The circular ramp looks something like this. My poor attempt at ASCII art
Justin Parke
Oakland Mills High School
Columbia, MD
-----Original Message-----
From: fizix29@aol.com
To: phys-l@carnot.physics.buffalo.edu
Sent: Thu, 26 Oct 2006 12:47 PM
Subject: [Phys-l] time to bottom of ramp
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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