The first harmonic would be the smallest frequency for a string to produce a standing wave. In addition, the strings were fixed in a single attachment and have only limited motion. It is because standing waves require a specific medium for the sound to travel in it.
Answer:
Part(a): The value of the spring constant is .
Part(b): The work done by the variable force that stretches the collagen is .
Explanation:
Part(a):
If '' be the force constant and if due the application of a force '' on the collagen '' be it's increase in length, then from Hook's law
Also, Young's modulus of a material is given by
where '' is the area of the material and '' is the length.
Comparing equation () and () we can write
Here, we have to consider only the circular surface of the collagen as force is applied only perpendicular to this surface.
Substituting the given values in equation (), we have
Part(b):
We know the amount of work done () on the collagen is stored as a potential energy () within it. Now, the amount of work done by the variable force that stretches the collagen can be written as
Substituting all the values, we can write
Answer:
k1 + k2
Explanation:
Spring 1 has spring constant k1
Spring 2 has spring constant k2
After being applied by the same force, it is clearly mentioned that spring are extended by the same amount i.e. extension of spring 1 is equal to extension of spring 2.
x1 = x2
Since the force exerted to each spring might be different, let's assume F1 for spring 1 and F2 for spring 2. Hence the equations of spring constant for both springs are
k1 = F1/x -> F1 =k1*x
k2 = F2/x -> F2 =k2*x
While F = F1 + F2
Substitute equation of F1 and F2 into the equation of sum of forces
F = F1 + F2
F = k1*x + k2*x
= x(k1 + k2)
Note that this is applicable because both spring have the same extension of x (I repeat, EXTENTION, not length of the spring)
Considering the general equation of spring forces (Hooke's Law) F = kx,
The effective spring constant for the system is k1 + k2
Answer:
0.333 i1
Explanation:
from figure
iB = i2
i1 = iA
i1 = iA = iB+iC = i2+iC
all resistances are equal o R
i1 = E/[R + 2R||R + R] = E/[8R/3] = 3E/8R
since if v is constant then i is inversely proportional to R
iB/iC = R/2R = 1/2
iC = 2iB = 2i2
and i1 = iB+iC = iB+2iB => i1 = 3iB = 3i2
thus i2 = i1/3
or
the equivalent resistance is
Req = [R || (R+R) ] + ( R + R)
Req = 2R/3 + 2R = 8R/3 ohm
current i1 = E / Req = E / ( 8R/3) = 3E/8R
i1 is divided in two parts as i2 = ib and ic
i1 is divided in i2 and ic in ratio 1 :2
Twice the current will flow through RC as will flow through RB and R2. So the current flowing in R1 and RA is divided by 3,
so i2 is 0.33*i1
i2 = [ 1 / (1+2) ] * i1 = 1/3 * i1
i2 = i1 / 3 = 0.333 i1