Answer:
y= 240/901 cos 2t+ 8/901 sin 2t
Explanation:
To find mass m=weighs/g
m=8/32=0.25
To find the spring constant
Kx=mg (given that c=6 in and mg=8 lb)
K(0.5)=8 (6 in=0.5 ft)
K=16 lb/ft
We know that equation for spring mass system
my''+Cy'+Ky=F
now by putting the values
0.25 y"+0.25 y'+16 y=4 cos 20 t ----(1) (given that C=0.25 lb.s/ft)
Lets assume that at steady state the equation of y will be
y=A cos 2t+ B sin 2t
To find the constant A and B we have to compare this equation with equation 1.
Now find y' and y" (by differentiate with respect to t)
y'= -2A sin 2t+2B cos 2t
y"=-4A cos 2t-4B sin 2t
Now put the values of y" , y' and y in equation 1
0.25 (-4A cos 2t-4B sin 2t)+0.25(-2A sin 2t+2B cos 2t)+16(A cos 2t+ B sin 2t)=4 cos 20 t
So by comparing the coefficient both sides
30 A+ B=8
A-30 B=0
So we get
A=240/901 and B=8/901
So the steady state response
y= 240/901 cos 2t+ 8/901 sin 2t
L = 1.00 m, the original length
A = 0.5 mm² = 0.5 x 10⁻⁶ m², the cross sectional area
E = 2.0 x 10¹¹ n/m², Young's modulus
P = 1500 N, the applied tension
Calculate the stress.
σ = P/A = (1500 N)/(0.5 x 10⁻⁶ m²) = 3 x 10⁹ N/m²
Let δ = the stretch of the string.
Then the strain is
ε = δ/L
By definition, the strain is
ε = σ/E = (3 x 10⁹ N/m²)/(2 x 10¹¹ N/m²) = 0.015
Therefore
δ/(1 m) = 0.015
δ = 0.015 m = 15 mm
Answer: 15 mm
Answer:
Magnetic field at the center of the loop 
Explanation:
It is given that total length of wire is 2 m and number of circular loop is 5 turns.
Therefore ,
We know , magnetic field at the center of loop is given by :
Putting all values in above equation we get :
Hence , this is the required solution.
Answer:
To calculate the age of a piece of bone
Explanation:
Carbon 14 is an isotope of carbon that is unstable and decays into Nitrogen 14 by emitting an electron. The decay rate of radioactive material is normally expressed in terms of its "half-life" (the time required by half the radioactive nuclei of a sample to undergo radioactive decay). The nice thing about carbon 14 is that its "half-life" is about 5730 years, which gives a nice reference to measure the age of fossils that are some thousand years old.
Carbon 14 dating is used to determine the age of objects that have been living organisms long ago. They measure how much carbon 14 is left in the object after years of decaying without having exchange with the ambient via respiration, ingestion, absorption, etc. and therefore having renewed the normal amount of carbon 14 that is in the ambient.
A rock is not a living organism, so its age cannot be determined by carbon 14 dating.
