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. A nylon is implanted into the abdominal cavity of a subject animal. The suture was removed after 10 days and a second piece of the same suture was removed after 20 days, and its average tensile strength was measured. The strength decreased by 40 and 50% respectively. How long will it take for the strength to decay 60% of its original strength? Assume an exponential decay of strength Hint: o/60= Aexp(-Bt)

. A nylon is implanted into the abdominal cavity of a subject animal. The suture was removed after 10 days and a second piece of the same suture was removed after 20 days, and its average tensile strength was measured. The strength decreased by 40 and 50% respectively. How long will it take for the strength to decay 60% of its original strength? Assume an exponential decay of strength Hint: o/60= Aexp(-Bt)

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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### Tensile Strength Decay in Sutures **Scenario**: A nylon is implanted into the abdominal cavity of a subject animal. The tensile strength of the suture is monitored over time to understand its decay rate. **Procedure**: - A first piece of the suture is removed after 10 days. - A second piece of the same suture is removed after 20 days. - The average tensile strength of both pieces is measured. **Observations**: 1. After 10 days, the suture's tensile strength decreased by 40%. 2. After 20 days, the tensile strength decreased by 50%. **Question**: How long will it take for the strength to decay by 60% from its original strength? **Assumption**: Assume the tensile strength decays exponentially. The strength decay formula given is: \[ \frac{\sigma_t}{\sigma_0} = A \exp(-Bt) \] **Solution**: The calculated time for the tensile strength to decay by 60% is: \[ \boxed{33 \text{ days}} \] **Explanation of Terms**: - \( \sigma_t \): The tensile strength at time \( t \). - \( \sigma_0 \): The initial tensile strength. - \( A \) and \( B \): Constants to be determined based on the decay observations. - \( t \): Time. **Mathematical Background**: This question leverages the principle of exponential decay, commonly used in various biological and physical processes to describe how a quantity decreases over time. The formula provided is a typical representation of exponential decay in material strength under physiological conditions. The constants \( A \) and \( B \) are typically derived from the data points provided.
Transcribed Image Text:### Tensile Strength Decay in Sutures **Scenario**: A nylon is implanted into the abdominal cavity of a subject animal. The tensile strength of the suture is monitored over time to understand its decay rate. **Procedure**: - A first piece of the suture is removed after 10 days. - A second piece of the same suture is removed after 20 days. - The average tensile strength of both pieces is measured. **Observations**: 1. After 10 days, the suture's tensile strength decreased by 40%. 2. After 20 days, the tensile strength decreased by 50%. **Question**: How long will it take for the strength to decay by 60% from its original strength? **Assumption**: Assume the tensile strength decays exponentially. The strength decay formula given is: \[ \frac{\sigma_t}{\sigma_0} = A \exp(-Bt) \] **Solution**: The calculated time for the tensile strength to decay by 60% is: \[ \boxed{33 \text{ days}} \] **Explanation of Terms**: - \( \sigma_t \): The tensile strength at time \( t \). - \( \sigma_0 \): The initial tensile strength. - \( A \) and \( B \): Constants to be determined based on the decay observations. - \( t \): Time. **Mathematical Background**: This question leverages the principle of exponential decay, commonly used in various biological and physical processes to describe how a quantity decreases over time. The formula provided is a typical representation of exponential decay in material strength under physiological conditions. The constants \( A \) and \( B \) are typically derived from the data points provided.
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