Total energy associated with a spring:
When x = 0.5a:
The ratio:
When x = 0.5a:
The ratio:
Consider an electron with charge −e and mass m orbiting in a circle around a hydrogen nucleus (a single proton) with charge +e.
1 answer:
Result:
,
Explanation:
The electromagnetic attraction between the electron and the proton in the nucleus is equivalent to the centripetal force:
where
k represents the Coulomb constant
e denotes the charge of the electron
e denotes the charge of the proton in the nucleus
r signifies the distance from the electron to the nucleus
v indicates the velocity of the electron
is the mass of the electron
Rearranging for v, we determine
Inside a hydrogen atom, the distance separating the electron from the nucleus is roughly
while the mass of the electron is
and the charge is
By plugging in the values into the formula, we achieve
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Answer:
According to the guideline for kilometers, every three seconds between a lightning strike and the subsequent thunder indicates the distance to the flash in kilometers.
Explanation:
To calculate the speed of sound in meters per second, we need to utilize certain conversion factors. One mile corresponds to 5 seconds after witnessing the lightning. Furthermore, 1 mile comprises 5280 feet, and 1 foot is equivalent to 0.3048 meters. This information is sufficient to solve the issue. The conversion ratios can be set up like this:
Observe how the ratios are organized such that the units cancel out during calculations. One ratio has miles in the numerator while the other has them in the denominator, leading to cancellation. The same applies to the feet.
The question requires us to provide the answer to one significant figure, resulting in the speed of sound rounding to 300m/s.
For the second part, we will again utilize conversions. This time we will set our ratios in reverse and realize that there are 1000 meters in 1 kilometer, leading us to:
This signifies that for every 3.11 seconds, the distance to the lightning strike is 1 kilometer. Since this is a fabric of general knowledge, we round to the nearest whole number for simplicity, establishing the guideline:
According to the rule for kilometers, every three seconds between a lightning flash and the following thunder gives the distance to the flash in kilometers.
Answer:
The beats frequency measures approximately
4.4 kHzExplanation:
The beat frequency arises from the original ultrasound frequency, , and the frequency of the sound reflected off the car,
:
(1)
To calculate the frequency of the reflected sound, we apply the Doppler effect formula:
where
v = 340 m/s, the speed of sound
is the velocity of the car
is the frequency of the sound emitted
By substituting values,
Thus, the beat frequency (1) is