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quester [9]
3 years ago
13

Using dimensional analysis, construct a constant, with units of length only, out of all three of the following fundamental const

ants of Nature: ℏ, ????, and c. Here, ℏ is Planck's constant, which has dimensions of [????][????]2[T]−1, ???? is Newton's gravitational constant, which has dimensions of [????]−1[????]3[T]−2, and c is the speed of light, with dimensions [????][T]−1.
Physics
1 answer:
ludmilkaskok [199]3 years ago
4 0

The quantity with units of length only is \sqrt{\frac{hG}{c^3}}

Explanation:

We have to combine the following constants:

- h, Planck constant, with units [m^2][kg][s^{-1}]

- G, the Newton's gravitational constant, with units [m^3][kg^{-1}][s^{-2}]

- c, the speed of light, with units [m][s^{-1}]

The combination of these constant should have units of length only, so with meters (m).

First, we notice that h has [kg] in its units, while G has [kg^{-1}] in its units, so in order to make the [kg] disappear, we have to multiply them and they should have same power, so:

hG = [m^{2+3}][kg^{1-1}][s^{-1-2}]=[m^5][s^{-3}]

Now we have to make the seconds, [s], disappear. We do that by dividing the new quantity by c^3, so that the new units are:

\frac{hG}{c^3}=\frac{[m^5][s^{-3}]}{([m][s^{-1}])^3}=\frac{[m^5][s^{-3}]}{[m^3][s^{-3}]}=[m^2]

We are almost done: now the quantity has units of an area, squared meters. Therefore, in order to make it have it units of length, we just take its square root:

\sqrt{\frac{hG}{c^3}}=\sqrt{[m^2]}=[m]

Learn more about gravitational constant:

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Different between progressive wave and stationary wave​
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1) Progressive waves are the ones by which all the wave disturbances are carried on further and propelled or transferred forward.

1) Stationary waves are the ones by which all the wave disturbances are not carried on further and propelled or transferred forward.

2) In Progressive waves the energies are equally and efficiently transferred along the travelling waves. Every particle are transferring some kind of energy to a next further particle on the same path, basically most of the energies are lost because of which there's no energy acquired by it.

2) In Stationary or standing waves there's no absolute transfer of any significant amount of energies which are not transferred along a path of the wave. Particles in stationery waves are giving and contributing in energy submission and also acquire some of the energy back because of which the net transferring of energies between the particles in a specific period as nullified.

3) Phases of the progressive waves of the particles in these waves are varying in a continuous manner and have changing values between them.

3) Phases of the Stationary or standing waves of the particles in these waves are not changing and always same to the contrary opposite when placed between the consecutively running sets of nodes (Between two nodes of particles).

4) Progressive waves have no particles which show they're having a rest phase or a permanent rest phase in a medium (particle medium).

4) Stationary waves have significant amount of particles of the medium to show that there having a rest phase or a permanent rest phase at the nodes of those particles.

5) Amplitudes of Progressive waves are totally and completely different particles are neutral and are having same values.

5) Amplitudes of Stationary or Standing waves of the particles in between those tow consecutively sets of nodes in between them and antinodes provided are having different values and vary much more progressively.

6) All of the particles in Progressive waves containing it don't specially cross their given mean positions in a simultaneous manner.

6) All of the particles in Stationary waves containing it frequently and steadily cross their given mean positions in a simultaneous manner.

7) In Progressive waves the particles don't show any attainment of a displacement provided in a maximum amount in a simulations manner.

7) In Stationary waves the particles are showing and exhibiting the attainments of various displacements in a maximum amount in a simultaneous manner.

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7 0
3 years ago
A person stands 6.00 m from a speaker, and 8.00 m from an identical speaker. What is the wavelength of the first (n=1) interfere
dalvyx [7]

Answer:

wavelength = 4 m

Explanation:

For distance 6 and 8m and speed of sound in air = c.

The travel time form the various distances 6 and 8 are 6/c and 8/c respectively.

cos(wt1) + cos(wt2) = 0

for a shift in phase t1 = t - 6/c,

t2 = t - 8/c

substituting t1 and t2

cos(π - w(t - 8/c)) = cos(w(t - 6/c))

solving using trigonometry identities in radians.

we have,

π - 2πn = w(t - 8/c) - w(t - 6/c)

putting w = 2πf

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dividing both sides by π

1 - 2n = 2ft - 16(f/c) - 2ft + 12(f/c)

simplifying we have,

1 - 2n = -4(f/c)

solving for f we have,

f = c/4(2n - 1)

putting n=1 and c = 343m/s

f = (343/4)*(2(1) - 1)

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What is the pressure 100m below the surface of the sea , if the density of sea water is 1150kg/m3
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The current theory of the structure of the
IRISSAK [1]

1) The mass of the continent is 3.3\cdot 10^{21} kg

2) The kinetic energy of the continent is 624 J

3) The speed of the jogger must be 4 m/s

Explanation:

1)

We start by finding the volume of the continent. We have:

L = 5850 km = 5.85\cdot 10^6 m is the side

t = 35 km = 3.5\cdot 10^4 m is the depth

So the volume is

V=L^2 t = (5.85\cdot 10^6)^2 (3.5\cdot 10^4)=1.20\cdot 10^{18} m^3

We also know that its density is

d=2750 kg/m^3

Therefore, we can find the mass by multiplying volume by density:

m=dV=(2750)(1.20\cdot 10^{18})=3.3\cdot 10^{21} kg

2)

The kinetic energy of the continent is given by:

K=\frac{1}{2}mv^2

where

m=3.3\cdot 10^{21} kg is its mass

v = 3.2 cm/year is the speed

We have to convert the speed into m/s. We have:

3.2 cm = 0.032 m

1 year = 1(365)(24)(60)(60)=3.15\cdot 10^7 s

So, the speed is:

v=\frac{0.032 m}{3.15 \cdot 10^7 s}=1.02\cdot 10^{-9} m/s

So, we can now find the kinetic energy:

K=\frac{1}{2}(1.20\cdot 10^{21})(1.02\cdot 10^{-9})^2=624 J

3)

Here we have a jogger of mass

m = 78 kg

And the jogger has the same kinetic energy of the continent, so

K = 624 J

The kinetic energy of the jogger is given by

K=\frac{1}{2}mv^2

where v is the speed of the jogger.

Solving for v, we find the speed that the jogger must have:

v=\sqrt{\frac{2K}{m}}=\sqrt{\frac{2(624)}{78}}=4 m/s

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