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3 years ago

Which of these equations is dimensionally correct?

Physics

1 answer:

8_murik_8 [283]3 years ago

3 0

Answer: first and third.

Explanation:

An equation is dimensionally correct if the units are the same in both sides of the equation.

first, let's define the units used:

{m} = kg

{v} = m/s

{F} = kg*m/s^2

{x} = m

{t} = s

{a} = m/s^2

Now, let's analyze each option:

1) m*v/t = F

in the left side the units are:

{m}*{v}/{t} = kg*(m/s)*(1/s) = kg*m/s^2

And as is written above, these are the units of F, so this is correct.

2) x*v^2 = F*(x^3/x^2)

This is more trivial, in the right side we can see an F, that has mass units (kg) and in the left side we have x and v, and we know that none of these have mass units, so this expression is not correct.

3) xt= vt^2+at^3

the units in the right side are:

{x}*{t] = m*s

in the right side are:

{v}*{t}^2 + {a}*{t}^2 = (m/s)*s^2 + (m/s^2)*s^3 = m*s + m*s

So in both sides of the equation we have the same units, then this equation is dimensionally correct.

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a vector is 253 m long and points in a 55.8 degree direction, what’s the y and x- component of the vector?

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Well we know the hypotenuse of the triangle which is 253 m. And we know the angle of the triangle which is 55.8 degrees. So we want to find y. And to find y we use sin. And sin is a ratio, the ratio of the opposite leg, and hypotenuse. So sin(55.8) = y/253. Now we solve for y by multiplying both sides by 253. And finally we get 209.25 as the length of the y component.

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A light wave moves from diamond (n= 2.4) into water (n= 1.33) at an angleof 24°. what angle does it have in water?

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Answer:

n1 sin θ1 = n2 sin θ2 Snell's Law (θ1 is the angle of incidence)

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2 years ago

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Answer:

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Explanation:

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3 years ago

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3 years ago

An example of when total internal reflection occurs is when all the light passing from a region of higher index of refraction to

Amiraneli [1.4K]

Answer:

is reflected back into the region of higher index

Explanation:

Total internal reflection is a phenomenon that occurs when all the light passing from a region of higher index of refraction to a region of lower index is reflected back into the region of higher index.

According to Snell's law, refraction of ligth is described by the equation

$n_1 sin \theta_1 = n_2 sin \theta_2$

where

n1 is the refractive index of the first medium

n2 is the refractive index of the second medium

$\theta_1$ is the angle of incidence (in the first medium)

$\theta_2$ is the angle of refraction (in the second medium)

Let's now consider a situation in which

$n_1 > n_2$

so light is moving from a medium with higher index to a medium with lower index. We can re-write the equation as

$sin \theta_2 = \frac{n_1}{n_2}sin \theta_1$

Where $\frac{n_1}{n_2}$ is a number greater than 1. This means that above a certain value of the angle of incidence $\theta_1$ , the term on the right can become greater than 1. So this would mean

$sin \theta_2 > 1$

But this is not possible (the sine cannot be larger than 1), so no refraction occurs in this case, and all the light is reflected back into the initial medium (total internal reflection). The value of the angle of incidence above which this phenomen occurs is called critical angle, and it is given by

$\theta_c =sin^{-1}(\frac{n_2}{n_1})$

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3 years ago