Final answer:
To calculate the amount by which the thread stretches, we need to use Hooke's Law and Young's modulus.
Step-by-step explanation:
To calculate the amount by which the thread stretches, we need to use Hooke's Law, which states that the force required to stretch or compress a spring by a distance is directly proportional to that distance. In this case, the thread is behaving like a spring when the spider hangs from it.
Using the formula for Young's modulus, we can calculate the force applied to stretch the thread:
F = (Y * A * ΔL) / L
where F is the force, Y is Young's modulus, A is the cross-sectional area of the thread, ΔL is the change in length of the thread, and L is the original length of the thread.
Given the mass of the spider, we can calculate the force:
F = m * g
where m is the mass of the spider and g is the acceleration due to gravity.
By equating these two forces, we can solve for ΔL:
(Y * A * ΔL) / L = m * g
Rearranging the equation, we find:
ΔL = (m * g * L) / (Y * A)
Plugging in the given values, we can calculate ΔL.