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

Fig. 10

1. Mechanics 17

tal surface. A similar hoop moves past it

at a velocity v.

Determine the velocity vA of the upper

point of "intersection" of the hoops as a func-

tion of the distance d between their centres,

assuming that the hoops are thin, and the

second hoop is in contact with the first hoop

as it moves past the latter.

1.25. A hinged construction consists of

three rhombs with the ratio of sides 3:2:1

(Fig. 10). Vertex A3 moves in the horizon-

tal direction at a velocity v.

Determine the velocities of vertices A 1 ,

A2, and B2 at the instant when the angles

of the construction are 90°

1.26. The free end of a thread wound on a

bobbin of inner radius r and outer radius R

is passed round a nail A hammered into

the wall (Fig. 11). The thread is pulled at a

constant velocity v.

Find the velocity vo of the centre of the

bobbin at the instant when the thread forms

an angle a with the vertical, assuming that

the bobbin rolls over the horizontal surface

without slipping.

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