document.write( "Question 1120006: A uniform wheel of 600mm diameter, weighing 5kN rests against a rigid rectangular block of 150mm height. Find the least pull, through the centre of the wheel, required just to turn the wheel over the corner A of a block. Also find the reaction of the block. Take all surfaces to be smooth \n" ); document.write( "

Algebra.Com's Answer #735801 by ikleyn(52817) $\"\"$ $\"About$

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\n" ); document.write( "A uniform wheel of 600mm diameter, weighing 5kN rests against a rigid rectangular block of 150mm height.
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\n" ); document.write( "Also find the reaction of the block. Take all surfaces to be smooth
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document.write( "Make a sketch. I will assume that you just did it and look in it.\r\n" );
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document.write( "The radius of the wheel is R = 300 mm 0.3 m.\r\n" );
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document.write( "The weight of 5 kN is applied at the center of the wheel and directed vertically down.\r\n" );
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document.write( "The force  F  (under the question) is applied horizontally at the center of the wheel. \r\n" );
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document.write( "As I said, it is directed horizontally, and it is directed to the block's side.\r\n" );
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document.write( "Draw the radius OA of the wheel from its center O to the point A where the wheel contacts with the block.\r\n" );
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document.write( "Notice that the angle the radius OA makes with the horizontal line is  = 30°.\r\n" );
document.write( "It is because the radius of the wheel is 300 mm,  while the height of the block is 150 mm.\r\n" );
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document.write( "The weight produces the moment of force  =  W*h,  where the arm \"h\" is the horizontal projection of the radius OA\r\n" );
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document.write( "    h =  = R*cos(30°).\r\n" );
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document.write( "Therefore the moment of force produced by the wheel's weight is  W*h =  Newtons*meter, \r\n" );
document.write( " where 0.3 = 0.3 m is the radius of the wheel.\r\n" );
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document.write( "The force F produces the moment   = F*0.15 Newtons*meter.\r\n" );
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document.write( "As you understand (or should understand), the moments of forces, produced by W and F, have opposite directions, and\r\n" );
document.write( "the equation for the least value of the horizontal force F, through the center of the wheel, required just to turn the wheel \r\n" );
document.write( "over the corner A of a block is the equality of magnitudes of the two moments of forces  (it is the key moment of the solution !)\r\n" );
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document.write( "    0.15*F = ,   or\r\n" );
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document.write( "    0.15*F = ,   which implies\r\n" );
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document.write( "    F =  =  Newtons.\r\n" );
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document.write( "Answer.  The least value of the horizontal force F, through the center of the wheel, required just to turn the wheel \r\n" );
document.write( "over the corner A of a block is  Newtons = 8660 Newtons  (approximately).\r\n" );
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document.write( "Regarding the reaction force from the block to the wheel,  it is directed along the radius OA from A to O and is equal to\r\n" );
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document.write( "     =  =  =  = 10 kilo-Newtons.\r\n" );
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\n" ); document.write( "\n" ); document.write( "P.S. Until I participate as a tutor in this forum, you can post any standard (or even non-standard) Physics problem. \r
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\n" ); document.write( "\n" ); document.write( "If it is formulated and presented correctly and professionally, I hope I can solve it
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\n" ); document.write( "\n" ); document.write( "Ability to solve practically ANY problem of the School, School+ and even School++ level in Physics and Math
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document.write( "    Those individuals who solved at the level  Math+++, were eligible to be enrolled without the entrance exams.\r\n" );
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document.write( "    Later, as a rule, they became professors at universities and some of them became Fields' award laureates in Math . . . \r\n" );
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