220 EXAMPLES. 



action of any force; for example, if the co t friction 



be 4, find the least number <t' turns which maybe Lrivm to 



vad on a cylinder 2 feet long and 6 inches in ( in uin- 



liesuh. Ki^lit. 



i'7. Two uniform beams of the same length ami mat. rial 

 placed in a vertical plane. :i state of rest bordering 



on motion under the following circumstances: their upper 

 ends are connected by a smooth hinge, about which they 

 can move freely; their other ends rest on a rough horizontal 

 plane, and the beams are perpendicular to each other: find 

 the coefficient of friction between the beams and the hori- 

 zontal plane. /i'<*n!t. p=\. 



28. A straight uniform beam is placed upon tv 

 planes whose inclinations to the horizon are a and a', and 

 the coefficients of friction tan \ and tan X'; shew that it ! 

 the limiting value of the angle of inclination of the Learn to 

 the horizon at which it will rest, W its weight, and R, Pi the 

 pressures upon the planes 



2 tan = cot (a + V) - cot (a - X), 

 R It W 



cos X sin (a' -f X') cos X' sin (a X) sin (a X + a' + X') " 



29. A heavy right cylinder is placed with its base on n 

 i horizontal plane, and is capable of motion n.uml its 



axis; find the least couple in a horizontal plane which will 

 move it. 



30. Two weights of different material arc laid on an in- 

 clined plane connected by a string extended to its full length. 

 inclined at an angle 6 to the line of intersection of the inclim -d 

 plane with the horizon; if the lower weight be on the point. 

 of motion find the magnitude and direction of the force of 

 friction on the upper weight. 



.". 1. A carriage stands upon four equal wheels ; Driven tho 

 coefficient of friction between the axles and the wheels find 

 the greatest slope on which it can remain at rest neglecting 

 weight of the wheels. 



