Answer: (a) The work done by this force on the particle is 42.71 J.
(b) The change in the potential energy of the system is -42.71 J.
(c) The kinetic energy the particle is 62.96 J.
Explanation:
(a) For the given situation, expression for work done is as follows.
W = 
= 
= ![[2\frac{x^{2}}{2} + 4x]^{5.15}_{0.9}](https://tex.z-dn.net/?f=%5B2%5Cfrac%7Bx%5E%7B2%7D%7D%7B2%7D%20%2B%204x%5D%5E%7B5.15%7D_%7B0.9%7D)
= 
= ![[(5.15)^{2} + 4(5.15) - (0.9)^{2} - 4(0.9)]](https://tex.z-dn.net/?f=%5B%285.15%29%5E%7B2%7D%20%2B%204%285.15%29%20-%20%280.9%29%5E%7B2%7D%20-%204%280.9%29%5D)
= 26.52 + 20.6 - 0.81 - 3.6
= 42.71 J
Hence, the work done by this force on the particle is 42.71 J.
(b) Expression for a conservative force is as follows.
F = 
dU = -Fdx
=
= -42.71 J
Therefore, the change in the potential energy of the system is -42.71 J.
(c) According to the work energy theorem,
W = 
= W
= 
where, u = velocity of the mass at x = 0.9 m
u = 3.0 m/s, m = 4.50 kg
As,
= 
= 62.96 J
Therefore, the kinetic energy the particle is 62.96 J.
<h2>Answer: Light waves have a redshift due to the Doppler effect
</h2>
The astronomer Edwin Powell Hubble observed several celestial bodies, and when obtaining the spectra of distant galaxies he observed the spectral lines were displaced towards the red (red shift), whereas the nearby galaxies showed a spectrum displaced to the blue.
From there, Hubble deduced that the farther the galaxy is, the more redshifted it is in its spectrum. <u>The same happens with the stars and this phenomenom is known as the Doppler effect.
</u>
This phenomenon refers to the change in a wave perceived frequency (or wavelength=color) when the emitter of the waves, and the receiver (or observer in the case of light) move relative to each other. For example, as a star moves away from the Earth, its espectrum turns towards the red.
Metals and properties of metals.
Answer:
a. Electric field lines can never cross each other.
d. Wider spacing between electric field lines indicates a lower magnitude of electric field.
Explanation:
a. The electric field lines cannot be crossed, since this would mean that there would be more than one electric field vector for the same point at the place where the crossing occurs.
d. The space between the field lines is inversely proportional to the intensity of the electric field.
Answer:
equipment for the measurement of microwave L bands with a range between 1 GHz and 2 GHz.
Explanation:
The electromagnetic spectrum can be calculated with the relationship between the speed of light, its wavelength and its frequency.
c = λ f
For reasons of analysis and equipment used, it is artificially divided into ranges, with poorly defined limits and in some cases with overlaps between some.
For the case of analysis, f = 1.41 10⁹ Hz, we have the range called
* Microwave for f> 3 108 Hz to approximately f <3 1011 Hz
For the lower part of the frequency 3 10⁸ <f <3 10⁹ Hz we have UHF television channels and cell phones and military communications.
As the frequency observed by the researchers is in the UHF range, it is possible that they are using microwave equipment for communications, specifically equipment for the measurement of microwave L bands with a range between 1 GHz and 2 GHz.
