Inclined planes increase the speed of objects going down it. draw two pictures- a slower object going down a regular platform and a speedier object zooming down an inclined plane.
Use the law of universal gravitation, which says the force of gravitation between two bodies of mass <em>m</em>₁ and <em>m</em>₂ a distance <em>r</em> apart is
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
where <em>G</em> = 6.67 x 10⁻¹¹ N m²/kg².
The Earth has a radius of about 6371 km = 6.371 x 10⁶ m (large enough for a pineapple on the surface of the earth to have an effective distance from the center of the Earth to be equal to this radius), and a mass of about 5.97 x 10²⁴ kg, so the force of gravitation between the pineapple and the Earth is
<em>F</em> = (6.67 x 10⁻¹¹ N m²/kg²) (1 kg) (5.97 x 10²⁴ kg) / (6.371 x 10⁶ m)²
<em>F</em> ≈ 9.81 N
Notice that this is roughly equal to the weight of the pineapple on Earth, (1 kg)<em>g</em>, where <em>g</em> = 9.80 m/s² is the magnitude of the acceleration due to gravity, so that [force of gravity] = [weight] on any given planet.
This means that on this new planet with twice the radius of Earth, the pineapple would have a weight of
<em>F</em> = <em>G m</em>₁ <em>m</em>₂ / (2<em>r</em>)² = 1/4 <em>G m</em>₁ <em>m</em>₂ / <em>r</em>²
i.e. 1/4 of the weight on Earth, which would be about 2.45 N.
Answer:
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22.5 J
Explanation:
Given:
x = 3 m
The spring potential energy is
The characteristics of the atomic spectrum allow to find the result so that the measured lines help the astronomer is:
- The astronomer can identify the gases that are present in stars using emission lines.
The emission spectrum is the emission of light due to the atomic transition in atoms, consequently the spectrum of each chemical element is unique.
The astronomer was able to identify the chemical elements that are in stars by their emission spectrum.
In the case presented there are two lines in the blue region, a line in the green region and a line in the red region. We know that the most abundant element in stars is hydrogen.
Hydrogen has a series of well-defined spectral lines, the series that is in the visible part of the spectrum is called the Balmer series and is composed of the lines in the table.
Color wavelength (nm)
red 656.3
blue 486.1
violet 434.1
The second element in quantity in stars is helium, which has the spectrum given in the table and in the attached.
color wavelength (nm)
Red 667.8
orange 587.6
green 501.6
Blue 492.2
Blue 447.1
The astronomer compares his measured spectrum with the spectra of these two gases and finds that the element he is measuring is helium.
In conclusion, using the characteristics of the atomic spectra, we can find the result to help the astronomer with the measured lines is:
- The astronomer can identify the gases that are present in stars using emission lines.
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