. 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
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ddf1e52-17d0-47a9-956c-00bd0ce93716%2F53a9fae3-fffc-404f-9d5e-3e057a2b04be%2Fc0k21pv_processed.jpeg&w=3840&q=75)
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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