The question is incomplete. The complete question is :
A viscoelastic polymer that can be assumed to obey the Boltzmann superposition principle is subjected to the following deformation cycle. At a time, t = 0, a tensile stress of 20 MPa is applied instantaneously and maintained for 100 s. The stress is then removed at a rate of 0.2 MPa s−1 until the polymer is unloaded. If the creep compliance of the material is given by:
J(t) = Jo (1 - exp (-t/to))
Where,
Jo= 3m^2/ GPA
to= 200s
Determine
a) the strain after 100's (before stress is reversed)
b) the residual strain when stress falls to zero.
Answer:
a)-60GPA
b) 0
Explanation:
Given t= 0,
σ = 20Mpa
Change in σ= 0.2Mpas^-1
For creep compliance material,
J(t) = Jo (1 - exp (-t/to))
J(t) = 3 (1 - exp (-0/100))= 3m^2/Gpa
a) t= 100s
E(t)= ΔσJ (t - Jo)
= 0.2 × 3 ( 100 - 200 )
= 0.6 (-100)
= - 60 GPA
Residual strain, σ= 0
E(t)= Jσ (Jo) ∫t (t - Jo) dt
3 × 0 × 200 ∫t (t - Jo) dt
E(t) = 0
That's true.
In fact, the resistance of a wire is given by:
where
is the resistivity of the material
L is the length of the wire
A is the cross-sectional area of the wire
We see that the resistance of the wire is inversely proportional to the cross-sectional area: A. Therefore, the narrower the wire, the smaller A, the larger the resistance. But higher resistance means that the current flowing through the wire is lower, therefore the flow of electrons in the circuit is slower, and the initial sentence is true.
Answer : Option C) Detective Smiley scanned the dim hallway. He pulled his pistol from its holster.
Explanation : Amongst the given other choices there seems to be no relationship between two consecutive sentences. The only sentence which seemed to have a connection between previous and later sentence was option C. Where it is clearly stated that the detective named as Smiley was walking through the hallway which was dimly lit. The second sentence has a co-relation to the previous one as it extends the sentence. Detective smiley then pulled out his pistol from his holster after walking through the hallway.
This confirms that the correct answer for this question is Option C.
Answer: option b.
Explanation:
The kinetic energy of a spring with constant K is calculated as:
kinetic energy = (k/2)*x^2
Where x^2 is the displacement of the spring with respect to it's rest position.
This can be written as a function like:
x = A*cos(2*pi*f*t)
where:
A is the amplitude (the maximum distance that the spring can move in each direction)
f is the frequency (and 2*pi*f is the angular frequency)
and t is the variable, it represents the time.
Replacing this in the kinetic energy equation, we get:
kinetic energy = (k/2)*(A*cos(2*pi*f*t))^2
This is the same as the option b: b. 1/2kA^2cos^2(2πft)
Then the corrrect option is b.