Sometimes, a crackling sound is heard while taking off a sweater during winters. Explain

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kozerog [31]

Newton's second equation of motion :-

S=ut+1/2at^2 [where, u is the initial velocity, a is the acceleration and t is the time interval]

This Equation simply finds a relation between distance travelled by a particle (classically) under uniform acceleration.

So let's see what pieces of information (bundles of equations) do we have with us, initially.

We have, a very primary equation with us,

dS/dt = v… (I)

(Considering motion in a straight line only)

And we also have the equation

dv/dt = a…(II)

Simply replacing the v in eqn (II) by eqn (I), we find

d2S/dt^2 = a…(III)

This is what we need to solve. It's easy.

You know,

d2S/dt^2 = d/dt(dS/dt) = a

⟹ dS/dt = ∫adt = at+c1

Since, dS/dt is the velocity of the particle,

Therefore, at t = 0, dS/dt|t = 0 = u

⟹ u = a∗0 + c1 = c1

⟹ c1 = u

Therefore, dS/dt = u + at

Thus, S = ∫(udt + atdt)

⟹ S = ut + 1/2at^2 +c^2

If say, the particle is already having a displacement S0 the moment you start measuring it's motion. Then, at t = 0, S = S0

This makes S = S0 +ut + 1/2at^2

Since, in most of the practical cases, we start measuring a motion when the particle starts displacing (i.e., when S0=0 ),

We get

S = ut + 1/2at^2

Hope it helps :)

5 0

3 years ago

The percent by which the fundamental frequency changed if the tension is increased by 30 percent is ? a)-20.04% b)-40.12% c)-30%

nika2105 [10]

Answer:

Percentage increase in the fundamental frequency is

d)-14.02%

Explanation:

As we know that fundamental frequency of the wave in string is given as

$f_o = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$

now it is given that tension is increased by 30%

so here we will have

$T' = T(1 + 0.30)$

$T' = 1.30T$

now new value of fundamental frequency is given as

$f_o' = \frac{1}{2L}\sqrt{\frac{1.30T}{\mu}}$

now we have

$f_o' = \sqrt{1.3}f_o$

so here percentage change in the fundamental frequency is given as

$change = \frac{f_o' - f_o}{f_o} \times 100$

% change = 14.02%

3 0

3 years ago

Write the equation in slope-intercept form <br> x-2y=4

maxonik [38]

Answer:

$y=\frac{1}{2}x-2$

Explanation:

Slope-intercept form means we want the y to be by itself in the equation. Every thing we do will be about getting the y alone on the left side of the equation

To start we should move x to the left hand side. We can do this by subtracting x from both sides. That way, there is an x on the right, but not the left.

x-x-2y=4-x

this gives us

-2y=4-x

Great! So now what? Well, the y isn't by itself yet because it still is being multiplied by negative two (-2). In order to move it from the left side to the right side, we have to do the opposite of multiply; divide. So, we will divide both sides by -2

$\frac{-2y}{-2} =\frac{4}{-2} -\frac{x}{-2}$

-2 divided by -2 is 1, 4 divided by -2 is -2, and -x divided by -2 is $\frac{1}{2}x$

This gives us the answer: $y=\frac{1}{2}x-2$

Tips:

A negative divided by a negative is a positive ex: -4 divided by -2 is positive 2

If you are subtracting by a negative number, you are actually adding by a positive ex: 2-(-2) is actually 2+2

Don't be afraid to have fractions in your equations

Whatever you do to the one side of the equation, you must do it to the other side as well. Multiply the left side by 2? You HAVE TO multiply the right side by two as well. Add 3 to the right side? You HAVE TO add 3 to the left.

For problems like this (and when you have access to the internet), where you need to rewrite an equation, double check your work on desmos, which is an online graphing calculator. Input both the original equation and the equation you rewrote, and if they don't create the same line, you did something wrong.

8 0

3 years ago

If continuous spectrum light from a star passes through a cool, low-density gas on its way to your telescope and spectroscope, _

natima [27]

Answer: a dark (absorption) line

Explanation:

This is as a result of absorption of electromagnetic a specific wavelength. The pattern followed by such lines is characteristic of specific atoms in the path of radiation.

6 0

3 years ago

What is the gravitational force between two 60.0 kg people sitting 100 m<br> apart?

Finger [1]

Answer:

2.4 × 10^(-11) N

Explanation:

F = Gm²/r²

F = 6.67×10^(-11) × 60² / 100²

= 2.4×10^(-11) N

7 0

4 years ago