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Eddi Din [679]
3 years ago
11

What fraction of the total energy of a SHO is kinetic when the displacement is one third the amplitude

Physics
1 answer:
Bas_tet [7]3 years ago
5 0

Answer:

The fraction of kinetic energy to the total energy is \frac{K}{T}=\frac{8}{9}.

Explanation:

displacement is one third of the amplitude.

Let the amplitude is A.

x= A/3

The kinetic energy of the body executing SHM is

K = 0.5 mw^2(A^2 - x^2)\\\\K = 0.5 m w^2 \left ( A^2 -\frac{A^2}{9} \right )\\\\K = 0.5 mw^2\times \frac{8A^2}{9}......(1)

The total energy is

T =0.5 mw^2A^2 ..... (2)

Divide (1) by (2)

\frac{K}{T}=\frac{8}{9}

You might be interested in
A spacecraft is in a circular Earth orbit at an altitude of 6000 km . By how much will its altitude decrease if it moves to a ne
blagie [28]

Answer:

a) 2148 km = 2150 km

b) 840 km

Explanation:

The force keeping the satellite in circular motion is the force given by Netwon's gravitational law

Centripetal force = (mv²/r)

Force due to Newton's law of gravitation = (GMm/r²)

where m = mass of satellite

M = mass of the earth

G = Gravitational constant

v = velocity of the satellite

r = radius of circular orbit

(mv²/r) = (GMm/r²)

v² = (GM/r)

Meaning that the square of the velocity of orbit is inversely proportional to the radius of circular orbit. (Since G and M are constants)

v² = (k/r)

when v = v₀, r = 6000 + 6378 = 12,378 km (the radius of orbit = 6000 km + radius of the earth)

v₀² = (k/12,378)

K = 12378v₀²

When the velocity increases by 10%, v₁ = 1.1v₀, the square of the new velocity = (1.1v₀)² = 1.21v₀² and the new radius of orbit = r₁

1.21v₀² = (k/r₁)

r₁ = (k/1.21v₀²)

Recall, k = 12378v₀²

r₁ = 12378v₀² ÷ 1.21v₀² = 10,229.75 km

10,229.75 km = (10,229.75 - 6378) km altitude above the Earth's surface

New altitude of orbit = 3851.75 km

Decrease in altitude = 6000 - 3851.75 = 2148 km

b) The period of orbit is related to the radius of orbit through Kepler's Law

T² ∝ R³

T² = kR³

When the period of orbit is T₀, Radius of orbit = R₀ = (6000 + 6378) = 12378 km (Earth's radius = 6378 km)

T₀² = kR₀³

T₀² = k(12378)³

k = (T₀²) ÷ (12378)³

When the period reduces by 10%, T₁ = 0.90T₀ and the new radius of orbit = R₁

T₁² = kR₁³

(0.90T₀)² = kR₁³

0.81T₀² = kR₁³

R₁³ = (0.81T₀²) ÷ k

Recall, k = (T₀²)/(12378)³

R₁³ = (0.81T₀²) ÷ [(T₀²)/(12378)³]

R₁³ = 1,536,160,005,663.1

R₁ = ∛(1,536,160,005,663.1) = 11,538.4 km

New Altitude = R₁ - (Radius of the Earth)

= 11,538.4 - 6378 = 5160.4 km

Decrease in altitude = 6000 - 5160.4 = 839.6 km = 840 km

Hope this Helps!!!

3 0
3 years ago
<img src="https://tex.z-dn.net/?f=help%20%5C%3A%20mo%20%5C%3A%20ako%20%5C%3A%20please.." id="TexFormula1" title="help \: mo \: a
morpeh [17]

bentar mo numpang cerita nih

jadi gini

eist yg takut cerita horor Jan di baca

awokawokawok

ok lanjut ya dek ke cerita nya :)

jadi gini di jalan,jalan lalu lintas di kampung,,,,em kyk gini,,,hmm...... kyk mana ku ceritakan ya dek,,,,bingung aku soalnya,,,,,hmm....kyk gini lah,,,,,,,,jalan ini di tengah² kebun/ladang nah kan,,,,, sebenarnya ada dua jalan mo pergi keluar masuk dari kampung ku ke kampung tetanga jadi pejalan kaki lebih suka lewat jalan tikus,,,,,yg punya mobil,kereta/motor,sepeda lewat jalan yg horornl itu yg kubilng tadi itu......,,,,nah,,,,,aku sama kawan²ku lewat jalan yg horor ini,,,,,,nah ngk nyangka ku lihat sosok putih,,,,y aku masih berpikir itu ngk bener ,,,,,trussss dua hari kemudian aku mo pergi ke kampung tetanga pake sepeda,,,,aneh ny sepeda aku berat dan,,,da-dan aku lihat sosok putih itu lagi ,,,aku jadi ngebut deh ,,,,Untung aja aku ngk jatuh ,,,,,klw di bilang suruk² ,,,setiap jalan aku ntah sama siapa² ttp ku lihat sosok putih itu,,,,nah ketika sore² aku jalan sama temen ku,,,,,eh ku lihat lagi,,,,aku penasaran aku aja deh temen ku buat nengok,,,sosok putih itu,,,,ngk nyangka sosok putih itu udh ngk ada ,,,,aneh ngab :v

dah lah sampe disini aja dulu ya dek

byee byee

............. ... .

6 0
2 years ago
Difina el concepto de salud
jeka94

Answer:bienestar mental y social. La mayoría de los padres conocen los conceptos básicos para mantener

Explanation:bienestar mental y social. La mayoría de los padres conocen los conceptos básicos para mantener a los niños sanos, como alimentarlos con alimentos saludables, asegurarse de que duerman y hagan suficiente ejercicio, y garantizar su seguridad.

5 0
3 years ago
Read 2 more answers
Olaf takes a picture of his dog using a digital camera. Which is true regarding the image of the dog detected by sensors in the
trasher [3.6K]

Answer: a. forms where light rays coming from the dog converge.

Explanation:

While photographing through digital camera, the light from the object through the lens converges and falls on image sensor.

The image breaks into many pixels and color and brightness of each pixel is measured and stored in form of number. This forms a digital image.

Thus, the correct option is a because the lens converges the light coming from the object onto the sensor.

6 0
3 years ago
Read 2 more answers
What type of units can be used for measurement?
Anna35 [415]

Answer:

Measurements most commonly use the International System of Units (SI) as a comparison framework. The system defines seven fundamental units: kilogram, metre, candela, second, ampere, kelvin, and mole.

3 0
3 years ago
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