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3 years ago

A sheet of gold foil has a volume of 0.750 cm3. If the foil measures 50.0cm by 10.0cm, what is the thickness of the foil?

Physics

1 answer:

vlada-n [284]3 years ago

6 0

To calculate the thickness of foil, we use formula of volume as

$V= l w t$

Here, l is the length of the foil, w is the width of the foil and t is the thickness of the foil.

Given, $V = 0.750 \ cm^3$ , $l = 50 cm$ and $w = 10 \ cm$ .

Substituting theses values in above equation, we get

$0.750 \ cm^3 = 50 cm \times 10 \ cm \times t \\\\ t = 0.0015 cm$

Thus, the thickness of the foil is 0.0015 cm.

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A mass of 1 slug, when attached to a spring, stretches it 2 feet and then comes to rest in the equilibrium position. Starting at

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Answer:

$Y=(\dfrac{3}{16}+t \dfrac{3}{8})e^{-2t}-\dfrac{3}{16}cos 4t$

Explanation:

Given that m= 1 slug and given that spring stretches by 2 feet so we can find the spring constant K

mg=k x

1 x 32= k x 2

K=16

And also give that damping force is 8 times the velocity so damping constant C=8.

We know that equation for spring mass system

my''+Cy'+Ky=F

Now by putting the values

1 y"+8 y'+ 16y=6 cos 4 t ----(1)

The general solution of equation Y=CF+IP

Lets assume that at steady state the equation of y will be

y(IP)=A cos 4t+ B sin 4t

To find the constant A and B we have to compare this equation with equation 1.

Now find y' and y" (by differentiate with respect to t)

y'= -4A sin 4t+4B cos 4t

y"=-16A cos 4t-16B sin 4t

Now put the values of y" , y' and y in equation 1

1 (-16A cos 4t-16B sin 4t)+8( -4A sin 4t+4B cos 4t)+16(A cos 4t+ B sin 4t)=6sin4 t

So by comparing the coefficient both sides

-16A+32B+16A=0 So B=0

-16 B-32 A+16B=6 So A=-3/16

y=-3/16 cos 4t

Now to find the CF of differential equation 1

y"+8 y'+ 16y=6 cos 4 t

Homogeneous version of above equation

$m^2+8m+16=0$

So $CF =(C_1+tC_2)e^{-2t}$

So the general equation

$Y=(C_1+tC_2)e^{-2t}-3/16 cos 4t$

Given that t=0 Y=0 So

$C_1=\dfrac{3}{16}$

t=0 Y'=0 So

$C_2 =\dfrac{3}{8}$

$Y=(\dfrac{3}{16}+t \dfrac{3}{8})e^{-2t}-\dfrac{3}{16}cos 4t$

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liberstina [14]

Answer:

P = 180.81 J

Explanation:

Given that,

Mass of a object, m = 4.1 kg

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Answer:

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