The figure represents an insect caught at the midpoint of a spider-web thread. T

Question

The figure represents an insect caught at the midpoint of a spider-web thread. The thread breaks under a stress of 9.2 × 108 N/m2 and a strain of 2.00. Initially, it was horizontal and had a length of 4.0 cm and a cross-sectional area of 9.5 × 10-12 m2. As the thread was stretched under the weight of the insect, its volume remained constant. If the weight of the insect puts the thread on the verge of breaking, what is the insect's mass? (A spider's web is built to break if a potentially harmful insect, such as a bumble bee, becomes snared in the web.)

a spider-web thread. The thread breaks under a stress of 9.2 x 106 N/m2 and a strain of 2.00. Initially, it was horizontal and h ght of the insect, its volume remained constant. If the weight of the insect puts the thread on verge break what is t the of mes snared in the web Open Show Work

Explanation / Answer

Here ,

tension in the cable is on the verge of breaking

tension in the wire = 9.5 *10^-12 * 9.2 *10^8

tension in the wire = 8.74 *10^-3 N

Now, final length of the wire = 2 * L + L = 3L

angle of wire with horizontal , theta = arccos(L/3L)

theta = 70.5 degree

Now, let the mass of insect is m

2 * T * sin(theta) = m * g

2 * 8.74 *10^-3 * sin(70.5 degree) = m * 9.8

m = 1.682 *10^-3 Kg

the mass of the insect is 1.682 *10^-3 Kg

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