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 2.25. The vertical axis scale is set by a = 0.130 GN/m²,b = 0.500 GN/m², and c = 0.720 GN/m². Assume that the thread has an initial length of 0.840 cm, an initial cross-sectional area of 4.00 × 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 would put the thread on the verge of breaking? What is the kinetic energy of (b) a fruit fly of mass 3.50 mg and speed 1.20 m/s and (c) a bumble bee of mass 0.420 g and speed 0.460 m/s? Would (d) the fruit fly and (e) the bumble bee break the thread?

a 0.950 1.30 2.25 Strain Stress (GN/m2)

Answer 1

- SF. dx = (stress) A (diblemental strain) - ALS(stress) (differental Strain) graph area - 4 as, + 1/2 (a+b) (S2-51) + (b+c)( 53-52) à Źr as, + b (53-51)+c/53-52)] - 5 0-130x109 (-30) + 0-500 mo [ 225 km] + 0.7200009 [2.25-1.30] c[ 0.169x709 +0-65x109 +0.634x10] a 0.7515x107 N/m at ka wa ALl graph area) a curio-12) (0.840x16² m) To Asisxio?) = 2.59504x10-5 J 67 kg a move tx [ 3.501106] [1.207 = 2.5241065 c) since ke cw , the fruit fly will not be able to break the thread d) Kb mor t 10.420* 15°) (0.460) 24.4426x16 a) on the other hand since ko sw the bumple Poce ceill be able to break the thread.