Answer: 0.0138 m^2 = 138 cm^2
Explanation:
The thermal expansion is the term use for the physical phenomena of dilation of the objects when they are exposed to changes in temperature.
The objects dilate when they are heated and contract when they are cooled.
The dilation is proportional to the change in temperatur.
For linear dilation, the proportionality constant is called linear dilation coefficient of the materials, it is named α and is measured in °C ^-1.
ΔL = α * Lo * ΔT, which means that the dilation (or contraction) is proportional to the product of the original length (Lo) and the change of temperature (ΔT).
There is also superficial dilation, for which the dilation is:
ΔA = β * Ao * ΔT, which means that the superficial dilation (or contraction) is proportional to the product of the original area (Ao) and the change of temperature (ΔT).
It is very interesting and important to solve problems that β = 2α, because regularly you will find the values of α for different materials and so, you just to multiply it times 2 to use β.
For this problem:
- Original area, Ao = area of the flat roof at - 10°C = 2.0m * 3.0m = 6.0 m^2.
- α for aluminum = 24 * 10^ -6 °C^-1.
- ΔT = 38°C - (-10°C) = 48°C
So, ΔA = 6.0m^2 * (2 * 24*10^-6 °C&-1) * 48°C = 0.0138 m^2
And that is the area that should stick out in summer to fit the structure during cold winter nights.
You can pass that number to cm^2 to grasp better the idea of this size:
0.0138 m^2 * (100 cm)^2 / m^2 = 138 cm^2
Complete question
The complete question is shown on the first uploaded image
Answer:
The velocity is 
Explanation:
From the question we are told that
a = nb
The length of the minor axis of the symbol of the Federation, a circle, seen by the observer at velocity v must be equal to the minor axis(b) of the Empire's symbol, (an ellipse)
Now this length seen by the observer can be mathematically represented as
Here t is the actual length of the major axis of of the Empire's symbol, (an ellipse)
So t = a = nb
and b is the length of the minor axis of the symbol of the Federation, (a circle) when seen by an observer at velocity v which from the question must be the length of the minor axis of the of the Empire's symbol, (an ellipse)
i.e h = b
So
![b = nb [\sqrt{1 - \frac{v^2}{c^2} } ]](https://tex.z-dn.net/?f=b%20%20%3D%20%20nb%20%20%5B%5Csqrt%7B1%20-%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D%20%7D%20%5D)
![[\frac{1}{n} ]^2 = 1 - \frac{v^2}{c^2}](https://tex.z-dn.net/?f=%5B%5Cfrac%7B1%7D%7Bn%7D%20%5D%5E2%20%3D%20%201%20-%20%20%5Cfrac%7Bv%5E2%7D%7Bc%5E2%7D)
![v^2 =c^2 [1- \frac{1}{n^2} ]](https://tex.z-dn.net/?f=v%5E2%20%3Dc%5E2%20%5B1-%20%5Cfrac%7B1%7D%7Bn%5E2%7D%20%5D)
![v^2 =c^2 [\frac{n^2 -1}{n^2} ]](https://tex.z-dn.net/?f=v%5E2%20%3Dc%5E2%20%5B%5Cfrac%7Bn%5E2%20-1%7D%7Bn%5E2%7D%20%5D)
Answer:
Explanation:
initial velocity, u = 0
final velocity, v = 60 mph = 26.8 m/s
time t = 10 s
Let a be the acceleration and s be he distance traveled.
Use first equation of motion
v = u + a t
26.8 = 0 + a x 10
a = 2.68 m/s
Use second equation of motion
s = ut + 1/2 at²
s = 0 + 0.5 x 2.68 x 10 x 10
s = 134 m
As, 1 m = 3.28 ft
So, s = 134 x 3.28 ft
s = 439.6 ft
