The formula for this problem that we will be using is:
F * cos α = m * g * μs where:F = 800m = 87g = 9.8
cos α = m*g*μs/F= 87*9.8*0.55/800= 0.59 So solving the alpha, find the arccos above.
α = arccos 0.59 = 54 ° is the largest value of alpha
Answer:
Intensity, ![I=1.101\ W/m^2](https://tex.z-dn.net/?f=I%3D1.101%5C%20W%2Fm%5E2)
Explanation:
Power of the light bulb, P = 40 W
Distance from screen, r = 1.7 m
Let I is the intensity of light incident on the screen. The power acting per unit area is called the intensity of the light. Its formula is given by :
![I=\dfrac{P}{A}](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7BP%7D%7BA%7D)
![I=\dfrac{P}{4\pi r^2}](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7BP%7D%7B4%5Cpi%20r%5E2%7D)
![I=\dfrac{40\ W}{4\pi (1.7\ m)^2}](https://tex.z-dn.net/?f=I%3D%5Cdfrac%7B40%5C%20W%7D%7B4%5Cpi%20%281.7%5C%20m%29%5E2%7D)
![I=1.101\ W/m^2](https://tex.z-dn.net/?f=I%3D1.101%5C%20W%2Fm%5E2)
So, the intensity of light is
.
Our values can be defined like this,
![m = 65kg](https://tex.z-dn.net/?f=m%20%3D%2065kg)
![v = 3.5m / s](https://tex.z-dn.net/?f=v%20%3D%203.5m%20%2F%20s)
![d = 0.55m](https://tex.z-dn.net/?f=d%20%3D%200.55m)
The problem can be solved for part A, through the Work Theorem that says the following,
![W = \Delta KE](https://tex.z-dn.net/?f=W%20%3D%20%5CDelta%20KE)
Where
KE = Kinetic energy,
Given things like that and replacing we have that the work is given by
W = Fd
and kinetic energy by
![\frac {1} {2} mv ^ 2](https://tex.z-dn.net/?f=%5Cfrac%20%7B1%7D%20%7B2%7D%20mv%20%5E%202)
So,
![Fd = \frac {1} {2} m ^ 2](https://tex.z-dn.net/?f=Fd%20%3D%20%5Cfrac%20%7B1%7D%20%7B2%7D%20m%20%5E%202)
Clearing F,
![F = \frac {mv ^ 2} {2d}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%20%7Bmv%20%5E%202%7D%20%7B2d%7D)
Replacing the values
![F = \frac {(65) (3.5)} {2 * 0.55}](https://tex.z-dn.net/?f=F%20%3D%20%5Cfrac%20%7B%2865%29%20%283.5%29%7D%20%7B2%20%2A%200.55%7D)
![F = 723.9N](https://tex.z-dn.net/?f=F%20%3D%20723.9N)
B) The work done by the wall is zero since there was no displacement of the wall, that is d = 0.
Answer:
I'm sorry but I dont really know this answer
Answer:
Given that
D= 4 mm
K = 160 W/m-K
h=h = 220 W/m²-K
ηf = 0.65
We know that
![m=\sqrt{\dfrac{hP}{KA}}](https://tex.z-dn.net/?f=m%3D%5Csqrt%7B%5Cdfrac%7BhP%7D%7BKA%7D%7D)
For circular fin
![m=\sqrt{\dfrac{4h}{KD}}](https://tex.z-dn.net/?f=m%3D%5Csqrt%7B%5Cdfrac%7B4h%7D%7BKD%7D%7D)
![m=\sqrt{\dfrac{4\times 220}{160\times 0.004}}](https://tex.z-dn.net/?f=m%3D%5Csqrt%7B%5Cdfrac%7B4%5Ctimes%20220%7D%7B160%5Ctimes%200.004%7D%7D)
m = 37.08
![\eta_f=\dfrac{tanhmL}{mL}](https://tex.z-dn.net/?f=%5Ceta_f%3D%5Cdfrac%7BtanhmL%7D%7BmL%7D)
![0.65=\dfrac{tanh37.08L}{37.08L}](https://tex.z-dn.net/?f=0.65%3D%5Cdfrac%7Btanh37.08L%7D%7B37.08L%7D)
By solving above equation we get
L= 36.18 mm
The effectiveness for circular fin given as
![\varepsilon =\dfrac{2\ tanhmL}{\sqrt{\dfrac{hD}{K}}}](https://tex.z-dn.net/?f=%5Cvarepsilon%20%3D%5Cdfrac%7B2%5C%20tanhmL%7D%7B%5Csqrt%7B%5Cdfrac%7BhD%7D%7BK%7D%7D%7D)
![\varepsilon =\dfrac{2\ tanh(37.08\times 0.03618)}{\sqrt{\dfrac{220\times 0.004}{160}}}](https://tex.z-dn.net/?f=%5Cvarepsilon%20%3D%5Cdfrac%7B2%5C%20tanh%2837.08%5Ctimes%200.03618%29%7D%7B%5Csqrt%7B%5Cdfrac%7B220%5Ctimes%200.004%7D%7B160%7D%7D%7D)
ε = 23.52