Answer:
(a) Angle of incidence for violet is more than the angle of incidence for red
(b) 2.4°
Explanation:
refractive index for violet , v = 1.66
refractive index for red, nR = 1.61
wavelength for violet, λv = 400 nm
wavelength for red, λR = 700 nm
Angle of refraction, r = 30°
(a) Let iv be the angle of incidence for violet.
Use Snell,s law
nv = Sin iv / Sin r
1.66 = Sin iv / Sin 30
Sin iv = 0.83
iv = 56°
Use Snell's law for red
nR = Sin iR / Sin r
where, iR be the angle of incidence for red
1.61 = Sin iR / Sin 30
Sin iR = 0.805
iR = 53.6°
So, the angle of incidence for violet is more than red.
(b) iv - iR = 56° - 53.6° = 2.4°
I can't seem to figure out the angle between T1 and T2. So suppose, it is 10º; then T2 makes an angle of 35º w/r/t horizontal, and T1 makes an angle of 45º.
Sum the moments about the base of the crane; Σ M = 0. 0 = T2*cos35*L*cos40 + T1*cos45*L*cos40 - T2*sin35*L*sin40 - T1*sin45*L*sin40 - W*(L/2)*sin40 - T1*L*sin40 → length L cancels where W = 18 kN
0 = 0.259*T2 - 43kN T2 = 166 kN
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
KE=1/2mv^2 - equation for kinetic energy
KE=(1/2)(0.12 kg)((7.8 m/s)^2 - plug it into the formula
KE=(0.06 kg)(60.84 m/s) - multiply 1/2 to the mass and square the speed
KE= 3.7 J - answer
Hope this helps
