perplexus.info :: Shapes : D on its side

D on its side (Posted on 2006-01-16)

If a solid semicylindrical block (a block-letter D) is placed on its curved side on a horizontal table, the top (the flat side) will be parallel to the table.

The table is tilted by an angle, a, perpendicular to the axis of the cylinder. What angle will the top of the block form with the table now?

Assume angle a is small enough to prevent the block from slipping or tipping over.

Submitted by Jer

Rating: 4.3333 (3 votes)

Solution: (Hide)

The center of mass (C) is (4r)/(3pi) from the flat edge. Call the point where the D touches the table T and the center of the flat edge O. We have the triangle COT with CT = (4r)/(3pi), OT=1 and angle T=a
Solving this triangle gives angle TOC = pi - arcsin((3pi/4)sin(a)) (It is obtuse) and angle COT= arcsin((3pi/4)sin(a)) - a
angle COT + a + pi/2 - x = pi/2 (x is the sought angle)
So x = a + arcsin((3pi/4)sin(a))
It has also been noted that the block will flip over at 25.11 degrees.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Answer	K Sengupta	2023-09-20 08:19:22
I have no clue what that means.	Brett Purcell	2006-03-09 20:13:52
I have no friggin idea.	Brett Purcell	2006-03-09 20:10:12
stupid answers	j	2006-01-23 22:10:07
re(2): Solution	Bractals	2006-01-17 11:00:49
re: Solution	Charlie	2006-01-17 10:35:03
re: Solution	Charlie	2006-01-17 10:07:25
Solution	Bractals	2006-01-17 01:43:39
Drunken master.	Percy	2006-01-16 23:28:18
Drunken master.	Percy	2006-01-16 23:27:56
Possible solution	Bractals	2006-01-16 22:41:51
Friction?	Richard	2006-01-16 20:23:33
re: Not really helpfull first thoughts	Richard	2006-01-16 19:40:09
Not really helpfull first thoughts	Hugo	2006-01-16 15:57:02

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