The figure shows an approximate plot of stress versus strain for a spider-web th
ID: 2263760 • Letter: T
Question
The figure shows an approximate plot of stress versus strain for a spider-web thread, out to the point of breaking at a strain of 2.00. The vertical axis scale is set by a
= 0.130 GN/m2,b = 0.340 GN/m2, and c = 0.900 GN/m2. Assume that the thread has an initial length of 0.880 cm, an initial cross-sectional area of 6.00
The figure shows an approximate plot of stress versus strain for a spider-web thread, out to the point of breaking at a strain of 2.00. The vertical axis scale is set by a = 0.130 GN/m2,b = 0.340 GN/m2, and c = 0.900 GN/m2. Assume that the thread has an initial length of 0.880 cm, an initial cross-sectional area of 6.00 times 10-12 m2, and (during stretching) a constant volume. The strain on the thread is the ratio of the change in the thread's length to that initial length, and the stress on the thread is the ratio of the collision force to that initial cross-sectional area. Assume also that when the single thread snares a flying insect, the insect's kinetic energy is transferred to the stretching of the thread. (a) How much kinetic energy (in ?J) would put the thread on the verge of breaking?Explanation / Answer
Total energy requred for breaking the thread per unit volume
= area under stress strain curve
= (1/2*0.130*0.75*10^9 + (1.45-0.75)/2*(0.13+0.34)*10^9 + (2-1.45)/2*(0.34+0.9)*10^9)
= 554.25*10^6
Total energy required = Energy per unit volume*Volume
= 29.2644*10^(-6) J
Ans = 29.2644
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