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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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BuyFindarrow_forward

College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A bimetallic strip of length L is made of two ribbons of different metals bonded together. (a) First assume the strip is originally straight. As the strip is warmed, the metal with the greater average coefficient of expansion expands more than the other, forcing the strip into an arc, with the outer radius having a greater circumference (Fig. P10.65). Derive an expression for the angle of bending, θ, as a function of the initial length of the strips, their average coefficients of linear expansion, the change in temperature, and the separation of the centers of the strips (Δr = r2r1). (b) Show that the angle of bending goes to zero when ΔT goes to zero and also when the two average coefficients of expansion become equal. (c) What happens if the strip is cooled?

images

Figure P10.65

(a)

To determine
The angle of bending ( θ ).

Explanation

Given info:

The length of the strip is L.

The change in temperature is ΔT .

The separation of the centers of the strips is,

Δr=r2r1 (I)

Formula to calculate the arc length ( L1 ) is,

L1=r1θ (II)

  • r1 is the radii of the arc.

Formula to calculate the arc length ( L2 ) is,

L2=r2θ (III)

  • r2 is the radii of the arc.

The arc length ( L1 ) is also expressed as,

L1=L[1+α1ΔT] (IV)

  • α1 is the co-efficient of linear expansion of ribbon-1

(b)

To determine
The value of θ when ΔT=0 and α1=α2 .

(c)

To determine
The effect of cooling of the strip.

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