Question

A wooden wheel of radius R is made of two semicircular parts (see figure)
sectional area S and I enath . 1 is slightly less than ?TR To fit the ring o
the wheel, it is heated so that its temperature rises by
AT and it just ste
cools down to surrounding temperature, it presses
the semicircular parts together. If the coefficient of linear expansion of the
metal is a, and its Young's modulus is Y, the force that one part of the
wheel applies on the other part is :

Answer 1

Explanation:

Radius =R

Cross-sectional area =S

Length =L

Temperature change =△T

Y is Young's Modulus

Coefficient of Linear expansion =α

Now, for the force that one part of the wheel applies on the other part is,

Y=

Strain

Stress

=

A△l

Fl

(1)

strain=

l

△l

=α△T

Putting values in equation (1)

Y=

Sα△T

F

F=SYα△T

From here, force is given.