Answer:
minimum length of a surface crack is 18.3 mm
Explanation:
Given data
plane strain fracture toughness K = 82.4 MPa m1/2
stress σ = 345 MPa
Y = 1
to find out
the minimum length of a surface crack
solution
we will calculate length by this formula
length = 1/π ( K / σ Y)²
put all value
length = 1/π ( K / σ Y)²
length = 1/π ( 82.4
/ 345× 1)²
length = 18.3 mm
minimum length of a surface crack is 18.3 mm
Answer:
the answer is 1.35. Have a nice day!!
Answer:
Joule
Explanation:
energy, work, quantity of heat
m2·kg·s-2
mass of iron block given as
![m_1 = 1.90 kg](https://tex.z-dn.net/?f=m_1%20%3D%201.90%20kg)
density of iron block is
![\rho = 7860 kg/m^3](https://tex.z-dn.net/?f=%5Crho%20%3D%207860%20kg%2Fm%5E3)
now the volume of the iron piece is given as
![V = \frac{m}{\rho}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7Bm%7D%7B%5Crho%7D)
![V = \frac{1.90}{7860} = 2.42* 10^{-4} m^3](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1.90%7D%7B7860%7D%20%3D%202.42%2A%2010%5E%7B-4%7D%20m%5E3)
Now when this iron block is complete submerged in oil inside the beaker the buoyancy force on the iron block will be given as
![F_b = \rho_L V g](https://tex.z-dn.net/?f=F_b%20%3D%20%5Crho_L%20V%20g)
here we know that
= density of liquid = 916 kg/m^3
![F_b = 916* 2.42 * 10^{-4} * 9.8](https://tex.z-dn.net/?f=F_b%20%3D%20916%2A%202.42%20%2A%2010%5E%7B-4%7D%20%2A%209.8)
![F_b = 2.17 N](https://tex.z-dn.net/?f=F_b%20%3D%202.17%20N)
Now for the reading of spring balance we can say the spring force and buoyancy force on the block will counter balance the weight of the block at equilibrium
![F_s + F_b = mg](https://tex.z-dn.net/?f=F_s%20%2B%20F_b%20%3D%20mg)
![F_s + 2.17 = 1.90* 9.8](https://tex.z-dn.net/?f=F_s%20%2B%202.17%20%3D%201.90%2A%209.8)
![F_s = 16.45 N](https://tex.z-dn.net/?f=F_s%20%3D%2016.45%20N)
So reading of spring balance will be 16.45 N
Now for other scale which will read the normal force of the surface we can write that normal force on the container will balance weight of liquid + container and buoyancy force on block
![F_n = F_g + F_b](https://tex.z-dn.net/?f=F_n%20%3D%20F_g%20%2B%20F_b)
![F_n = (1 + 2.50)*9.8 + 2.17](https://tex.z-dn.net/?f=F_n%20%3D%20%281%20%2B%202.50%29%2A9.8%20%2B%202.17)
![F_n = 34.3 + 2.17 = 36.47 N](https://tex.z-dn.net/?f=F_n%20%3D%2034.3%20%2B%202.17%20%3D%2036.47%20N)
So the other scale will read 36.47 N
The frequency of oscillation is 2.153 Hz
What is the frequency of spring?
Spring Frequency is the natural frequency of spring with a weight at the lower end. Spring is fixed from the upper end and the lower end is free.
For the mass-spring system in this problem,
The Frequency of spring is calculated with the equation:
![f = \frac{1}{2\pi } \sqrt{\frac{k}{m} }](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%7D%20%5Csqrt%7B%5Cfrac%7Bk%7D%7Bm%7D%20%7D)
Where,
f = frequency of spring
k = spring constant = 64 N/m
m = mass attached to spring = 350g = 0.350 kg
a = maximum acceleration = 5.3 m/s^2
Substituting the values in the equation,
![f = \frac{1}{2\pi } \sqrt{\frac{64}{0.350} }](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%7D%20%5Csqrt%7B%5Cfrac%7B64%7D%7B0.350%7D%20%7D)
![f = \frac{1}{2\pi } ( 13.522)](https://tex.z-dn.net/?f=f%20%3D%20%5Cfrac%7B1%7D%7B2%5Cpi%20%7D%20%28%2013.522%29)
![f = 2.1535 Hz](https://tex.z-dn.net/?f=f%20%3D%202.1535%20Hz)
Hence,
The frequency of oscillation is 2.153 Hz
Learn more about frequency here:
<u>brainly.com/question/13978015</u>
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