PLANE WITH FRICTION. 



/ 



lie cocffi. ii greater than *w equilibrium 



i all values of 6 between w - a and - . 

 1 1 . Suppose W greater than J\ so that k is greater than 



this case a is greater than e, and the equation 



sin (0 + <) - sin a 



has two solutions which may be admissible, namely, 

 -a, and 



The expression ,- g is always positive, and as in- 

 creases from to j the expression increases up to a maximum 



value and then decrease*. The maximum value is when 



1 1 Jt 



OM0-T, and is -7773 -r, that is, 



~ 

 Hence we shall obtain the following results : 



coefficient of friction is not less than 



will subsist for all values of between and > . 



p 



he coefficient of friction is less than -p, equilibrium 



will v.i:->: tor all values of between and a-e. 



P r 



* between -m and 



!>rium will subsist for all values of between and 

 a e, and between IT a c and . 



III. Suppose ir=/'. In this case there is equilibrium 



D 0-0, no fruti'm 1 exerted; and besides this 



we have results which may be deduced from those in the 



first case. Here a= B coefficient of friction is lev 



U 



