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Explanation:
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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
Answer:
The angular speed of the new system is .
Explanation:
Due to the absence of external forces between both disks, the Principle of Angular Momentum Conservation is observed. Since axes of rotation of each disk coincide with each other, the principle can be simplified into its scalar form. The magnitude of the Angular Momentum is equal to the product of the moment of inertial and angular speed. When both disks begin to rotate, moment of inertia is doubled and angular speed halved. That is:
Where:
- Moment of inertia of a disk, measured in kilogram-square meter.
- Initial angular speed, measured in radians per second.
- Final angular speed, measured in radians per second.
This relationship is simplified and final angular speed can be determined in terms of initial angular speed:
Given that , the angular speed of the new system is:
The angular speed of the new system is .
Answer:
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Explanation: