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A spider of mass 6.1 x 10 kg hangs from a 75.1 cm long thread whose diameter is 2.0 x 103 mm. Young's modulus of thread is 3x 10 N/m². By how much does the thread stretch (in m)?

User MDF
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1 Answer

4 votes

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.

User Waylan
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