The radius of the curved road at the given condition is 54.1 m.
The given parameters:
- <em>mass of the car, m = 1000 kg</em>
- <em>speed of the car, v = 50 km/h = 13.89 m/s</em>
- <em>banking angle, θ = 20⁰</em>
The normal force on the car due to banking curve is calculated as follows;
![Fcos(\theta) = mg](https://tex.z-dn.net/?f=Fcos%28%5Ctheta%29%20%3D%20mg)
The horizontal force on the car due to the banking curve is calculated as follows;
![Fsin(\theta) = \frac{mv^2}{r}](https://tex.z-dn.net/?f=Fsin%28%5Ctheta%29%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Br%7D)
<em>Divide </em><em>the second equation by the first;</em>
![\frac{Fsin(\theta)}{Fcos(\theta) } = \frac{mv^2}{rmg} \\\\tan(\theta) = \frac{v^2}{rg} \\\\r = \frac{v^2}{g \times tan(\theta)} \\\\r = \frac{13.89^2}{9.8 \times tan(20)} \\\\r = 54.1 \ m](https://tex.z-dn.net/?f=%5Cfrac%7BFsin%28%5Ctheta%29%7D%7BFcos%28%5Ctheta%29%20%7D%20%3D%20%5Cfrac%7Bmv%5E2%7D%7Brmg%7D%20%5C%5C%5C%5Ctan%28%5Ctheta%29%20%3D%20%5Cfrac%7Bv%5E2%7D%7Brg%7D%20%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7Bv%5E2%7D%7Bg%20%5Ctimes%20tan%28%5Ctheta%29%7D%20%5C%5C%5C%5Cr%20%3D%20%5Cfrac%7B13.89%5E2%7D%7B9.8%20%5Ctimes%20tan%2820%29%7D%20%5C%5C%5C%5Cr%20%3D%2054.1%20%5C%20m)
Thus, the radius of the curved road at the given condition is 54.1 m.
Learn more about banking angle here: brainly.com/question/8169892
Answer:
In 5 years or so, the sun will be awash in sunspots and more prone to violent bursts of magnetic activity.
Explanation
once the magnetic field weakens the area and cold plasma enters the area of the sunspot
At the present time, the only way we know of that light can get shifted
toward the blue end of the spectrum is the Doppler effect ... wavelengths
appear shorter than they should be when the source is moving toward us.
IF that's true in the case of the Andromeda galaxy, it means the galaxy is
moving toward us.
We use the same reasoning to conclude that all the galaxies whose light is red-shifted are moving away from us. That includes the vast majority of all galaxies that we can see, and it strongly supports the theory of the big bang
and the expanding universe.
If somebody ever comes along and discovers a DIFFERENT way that light
can get shifted to new, longer or shorter wavelengths, then pretty much all
of modern Cosmology will be out the window. There's a lot riding on the
Doppler effect !