Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

184 Aptitude Test Problems in Physics

From these relations, we can determine the angles

corresponding to the equilibrium position of the

system:

m2_m2,.... m^2

sin a2—

2 1 M^2 -MI+ MI

sin a 1 —^ , (^) •
2Mm^1 2Mm^2
Obviously, equilibrium can be attained only
under the conditions that 0 < al < 7E/2 and 0 <
a2 < 3t/2, i.e.

0< 2

m2 _m2+ m 2

' <1, 0 <

M2—mid-ml

<1.

2Mm 1 2Mm 2

These inequalities imply that the entire system

will be in equilibrium only provided that

M < m^1 + m^2 , M^2 > I — mil.

2. Let us consider the equilibrium of point A.
   At this point, flute forces are applied:

Ti = mi g, T2 = m 2 g, T3 = Mg.

Point A is in equilibrium when T1, T2, and T3 form

a triangle. Since the sum of two sides of a triangle

is larger than the third side, we obtain the relation

between the masses ml, m 2 , and M required 1. 4 - )

the equilibrium of point A:

+ ma > M, M ma > ma, M ma >

1.86. Let us consider the equilibrium conditions
for the rod at the instant when it forms an angle a
with the horizontal. The forces acting on the rod
are shown in Fig. 181. While solving this problem,
it is convenient to make use of the equality to zero
of the sum of the torques about the point of inter-
section of the force of gravity mg and the force F
applied by the person perpendicular to the rod
(point 0) since the moments of these forces abowt
this point are zero.
If the length of the rod is 21, the arm of the
normal reaction Nisi cos cc, while the arm of the