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

176 Aptitude Test Problems in Physics

where T 1 and T 2 are the tensions of the relevant

threads.

Let us write the equations of motion for the

two bodies in the vertical and horizontal directions:

T 1 sin a = m 1 w 211 sin a, T 1 cos a = ma,

T2 sin 6 = m 2 w 2 / 2 sin 0, T2 cos 6 = m 2 g.

Solving this system of equations and taking into

account Eq. (1), we obtain

g1/2 74 11/4

m 212 — map ) 1/y 14 rad/s.

2 2

1.76. We denote by 11 and / 2 the lengths of the

springs connecting the axle to the first ball and

the first and the second ball. Since the balls move

in a circle, their equations of motion can be writ-

ten in the form

m(1) 2 /1 = k ( 1 1 — 1 2) — k ( 1 2 — 1 2),

mw (^2) ( 1 1+ 1 2) = k ( (^1) 2 — lo),
whence
11_
1— 3mo)^2 1k+ (n.0^2 1k)^2 '
(1— mw 2 /k) / 0
/2 — 1 — 3mw 2 /k (mw 2 /k) 2 •
The solution has a physical meaning when the fol-
lowing inequalities are satisfied:
mw 2 mw 2
1 3
k > 0, 1— "2 O.
Let us suppose that mw 2 /k = x. Since mw 2 /k > 0,
the second condition implies that 0 < x < 1. The
first condition yields
x 2 — 3x 1 > 0,
whence either x > (3 + 1/)/2 2.6, or x <
(3 — 0)/2 ti Consequently, the region of