Obtain symbolic expressions for the maximum tensile and compressive stresses ( ómax,Tn and ómax,Cn )and their locations (coordinates xmax,T and xmax,C ) in terms of ñ, g, L (with ñ written as rho). (Note: enter the expressions for the stresses with their appropriate signs.)
ómax,Tn=
unanswered
at location xmax,T=
unanswered
ómax,Cn=
unanswered
at location xmax,C=
unanswered
To obtain the symbolic expressions for the maximum tensile and compressive stresses (ómax,Tn and ómax,Cn) and their locations (coordinates xmax,T and xmax,C) in terms of ñ, g, and L, we need to analyze the stress distribution in the given system.
The system is subjected to tensile stress when it elongates or is being pulled apart, and it undergoes compressive stress when it contracts or is being squeezed.
To find ómax,Tn, we need to calculate the maximum tensile stress. Since this stress occurs at the location of maximum elongation, we can determine it from the equation:
σmax,T = ñ * g * L.
Here, ñ represents rho, g is the gravitational acceleration, and L is the length of the system.
To find the location of this maximum tensile stress, xmax,T, we need to identify the position in the system where the elongation is maximum. This can be found using the parameter L/2.
Thus, the expressions for the maximum tensile stress and its location are:
ómax,Tn = ñ * g * L,
at location xmax,T = L/2.
On the other hand, to find ómax,Cn, the maximum compressive stress, we need to calculate the maximum contraction stress. This occurs at the location of maximum contraction or compression, which also corresponds to the center of the system.
So, the equation for ómax,Cn is:
ómax,Cn = -ñ * g * L/2.
The negative sign indicates the compressive nature of the stress. Similarly, the location of maximum compression, xmax,C, is also at the center of the system, given by:
at location xmax,C = 0.
To summarize:
ómax,Tn = ñ * g * L,
at location xmax,T = L/2.
ómax,Cn = -ñ * g * L/2,
at location xmax,C = 0.