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Delicious77 [7]

3 years ago

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A small logo is embedded in a thick block of crown glass (n = 1.52), 4.70 cm beneath the top surface of the glass. The block is

put under water, so there is 1.70 cm of water above the top surface of the block. The logo is viewed from directly above by an observer in air. How far beneath the top surface of the water does the logo appear to be?

1 answer:

harkovskaia [24]3 years ago

3 0

The concept required to solve this problem is the optical relationship that exists between the apparent depth and actual or actual depth. This is mathematically expressed under the equations.

$d'w = d_w (\frac{n_{air}}{n_w})+d_g (\frac{n_{air}}{n_g})$

Where,

$d_g =$ Depth of glass

$n_w =$ Refraction index of water

$n_g =$ Refraction index of glass

$n_{air} =$ Refraction index of air

$d_w =$ Depth of water

I enclose a diagram for a better understanding of the problem, in this way we can determine that the apparent depth in the water of the logo would be subject to

$d'w = d_w (\frac{n_{air}}{n_w})+d_g (\frac{n_{air}}{n_g})$

$d'w = (1.7cm) (\frac{1}{1.33})+(4.2cm)(\frac{1}{1.52})$

$d'w = 4.041cm$

Therefore the distance below the upper surface of the water that appears to be the logo is 4.041cm

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3.036×10⁻¹⁰ N

Explanation:

From newton's law of universal gravitation,

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Where F = Gravitational force between the balls, m1 = mass of the first ball, m2 = mass of the second ball, r = distance between their centers.

G = gravitational constant

Given: m1 = 7.9 kg, m2 = 6.1 kg, r = 2.0 m, G = 6.67×10⁻¹¹ Nm²/C²

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Does the sun always shine directly overhead at the equator at noon

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A mass of 0.5 kg hangs motionless from a vertical spring whose length is 1.10 m and whose unstretched length is 0.50 m. Next the

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The maximum length during the motion is $L_{max} = 1.45m$

Explanation:

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y is the difference in weight which is $=1.10-0.50=0.6m$

The negative sign is because the displacement of the spring (i.e its extension occurs against the force F)

Now substituting values accordingly

$k = \frac{4.9}{0.6}$

$= 8.17 N/m$

The elastic potential energy is given as $E_{PE} = \frac{1}{2} k D^2$

where D is this the is the displacement

Since Energy is conserved the total elastic potential energy would be

$E_T = initial \ elastic\ potential \ energy + kinetic \ energy$

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$4.085 * D_{max}^2 = 3.69$

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So to obtain total length we would add the unstretched length

So we have

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Earth has a mass of 5,970,000 how would scientists express this in a number scientific notation

Kazeer [188]

Taking into account the definition of Scientific notation, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.

<h3>Definition of scientific notation</h3>

Scientific notation is a quick way to represent a number using powers of base 10.

The numbers are written as a product:

a×10ⁿ

where:

a is a real number greater than or equal to 1 and less than 10, to which a decimal point is added after the first digit if it is a non-integer number.
n is a whole number, which is called an exponent or an order of magnitude. Represents the number of times the point decimal is shifted. It is always an integer, positive if it is shifted to the left, negative if it is shifted to the right.

<h3>This case</h3>

In this case, to write the number 5,970,000 in scientific notation, the following steps are performed:

The decimal point is moved to the left as many spaces until it reaches the right of the first digit. This number will be the value of a in the previous expression. Then a = 5.97
The base 10 is written with the exponent equal to the number of spaces that the decimal point moves. This is a positive number because the decimal point is shifted to the left, and it will have a value of n = 6.

Finally, the correct representation of 5,970,000 in scientific notation is 5.97×10⁶.

Learn more about scientific notation:

brainly.com/question/18073768

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