PHYSICS COLLEGE

Find an expression for the center of mass of a solid hemisphere, given as the distance R from the center of the flat part of the hemisphere. Express your answer in terms of R. Express the coefficients using three significant figures.

Answers

Answer 1

Answer:

z_c = ⅜R

Explanation:

If we assume that the hemisphere has uniform density, we can express the centre of mass as;

z_c = (ρ/M)∫∫∫ z•dV

We know that density(ρ) = mass(M)/volume(V)

Thus, Vρ = M

And volume of hemisphere = 2πr³/3

Thus;

2Vρπr³/3 = M

So;

z_c = (ρ/(2Vρπr³/3))∫∫∫ z•dV

Where r = R in this case.

ρ will cancel out to give;

z_c = (3/(2πr³))∫∫∫_V (z•dV)

In spherical coordinates,

r is radius

Φ = angle between the point and the z − axis

θ = azimuthal angle

Therefore, the integral becomes what it is in the attached image.

I've completed the explanation as well in the attachment.

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Which statement accurately describes the relationship between force and momentum?A. As the mass of an object increases its momentum increases, and it takes more force to change its motion. B. As the velocity of an object increases, its momentum decreases and it takes less force to change its motion.C. As the mass of an object increases its momentum decreases and it takes less force to change it motion D. As the velocity of an object decreases its momentum increases and it takes more force to change its motion

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Answers

Answer:

Answer

The Final Quality of teh R-134a in the container is 0.5056

The Total Heat transfer is $Q_(in) = 22.62 KJ$

Explanation:

Explanation is in the following attachments

Which of the following is not a motivation behind taking performance enhancing drugs?A.Having bigger, stronger muscles B.improving recovery time fir injuries C. Pumping

Answers

Answer:

C. Pumping

Explanation:

???

Answer: Losing weight due to decreased appetite

Explanation: because you guys trust me

Which volcanoes are formed by pyroclastic deposits? Select all that apply. A. cinder cone B. stratovolcano C. shield volcano

Answers

Answer:

Its a cinder cone cause after it all falls down to make deposits.

cinder cone and stratovolcano

You are measuring the volume of a chemical beaker how would u take the measurment? a.lift the beaker to eye level
b.you look down at the liquid above
c.use a ruler to measure
d.you squat to be eye level to the beaker

Answers

I think its d because lifting it would make the chemical swish around and that will make it so you cant get the right measurement. hope this helps :)

What is the speed of an electron with a de Broglie wavelength of 0.20 nm?

Answers

Answer:

$v = 3.65 * 10^6 m/s$

Explanation:

Given

de Broglie wavelength = 0.20nm

Required

Determine the speed (v)

The speed is calculated using the following formula;

$L = (h)/(mv)$

Where

$L = Wavelength = 0.2nm$

$h = Planck's\ constant = 6.63 * 10^(-34)Js$

$m = Mass\ of\ Electron = 9.11 * 10^(-31) kg$

Substitute these values in the above formula

$0.2nm = (6.63 * 10^(-34))/(9.11 * 10^(-31) * v)$

-----------------------------------------------------

Convert 0.2nm to metre (m)

$0.2nm = 0.2 * 10^(-9)m$

-----------------------------------------------------

$0.2 * 10^(-9) = (6.63 * 10^(-34))/(9.11 * 10^(-31) * v)$

Multiply both sides by v

$v * 0.2 * 10^(-9) = (6.63 * 10^(-34))/(9.11 * 10^(-31) * v) * v$

$v * 0.2 * 10^(-9) = (6.63 * 10^(-34))/(9.11 * 10^(-31) )$

$v * 0.2 * 10^(-9) = (0.73 * 10^(-34))/(10^(-31) )$

$v * 0.2 * 10^(-9) = 0.73 * 10^(-34) * 10^(31)$

Apply law of indices

$v * 0.2 * 10^(-9) = 0.73 * 10^(-34 + 31)$

$v * 0.2 * 10^(-9) = 0.73 * 10^(-3)$

Divide both sides by $0.2 * 10^(-9)m$

$v = (0.73 * 10^(-3) )/( 0.2 * 10^(-9) )$

$v = (3.65 * 10^(-3) )/(10^(-9) )$

Apply law of indices

$v = 3.65 * 10^(-3) * 10^9$

$v = 3.65 * 10^(-3+9)$

$v = 3.65 * 10^6$

Hence;

The velocity is

$v = 3.65 * 10^6 m/s$

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