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 3.5 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.)

Answer 1

Ultimate stress

Ultimate strain

Initial length

Initial cross-sectional area

When the thread goes down under the weight of insect, it gets elongated. Let the angle between thread and horizontal be .

Length of thread now

Since the thread is about to break, ultimate strain .

Hence

and

Since the volume is constant,

New area of cross-section .

Since the net force on insect is zero,

When the thread is about to break, Tension in the thread is

Weight of insect

Mass of insect