Response: k = 23045 N/m
Clarification:
To determine the spring constant, one must consider the maximum elastic potential energy that the spring can withstand. The kinetic energy of the vehicle should equal at minimum the elastic potential energy of the spring when it is fully compressed. Hence, we express it as:
(1)
The spring constant calculates to 23045 N/m
The rate equation for a first order reaction can be expressed as follows:
In this context, k represents the reaction's rate constant, t denotes the time the reaction takes, is the initial concentration, and
is the concentration at time t.
The rate constant of the reaction is .
(a) If we start with an initial concentration of 100, when 90% of the substance is eliminated, the remaining quantity at time t will be 100-90=10. By substituting the values,
The time required to destroy 90% of the substance amounts to 23.03 days.
(b) If the initial concentration is set at 100, when 99% is destroyed, the present amount at time t will be 100-99=1. By substituting the input values,
This results in a duration of 46.06 days required to eradicate 99% of the chemical.
(c) Should the initial concentration be set at 100, with 99.9% of the chemical removed, the remaining quantity at time t will be 100-99.9=0.1. Substituting the values yields
Thus, the time needed to eliminate 99.9% of the chemical is calculated as 69.09 days.