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A light spring of constant k = 90.0 N/m is attached vertically

A light spring of constant k = 90.0 N/m is attached vertically

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Please answer using a diagram or a drawing to throughly explain with clear explanations. If possible please use the formulas I provided.

4. A light spring of constant k = 90.0 N/m is attached vertically to a table. A balloon (with empty mass %3D 2.50 g) is filled with a mixture of helium (density = 0.179 kg/m³) and air (density = 1.29 kg/m³) to a volume of 4.00 m³ and is then connected to the spring, causing the spring to stretch. If the spring %3D %3D stretches by 1.0 cm, find the required density of the gas mixture, and find how much helium and air you need to produce that mixture.
Transcribed Image Text:4. A light spring of constant k = 90.0 N/m is attached vertically to a table. A balloon (with empty mass %3D 2.50 g) is filled with a mixture of helium (density = 0.179 kg/m³) and air (density = 1.29 kg/m³) to a volume of 4.00 m³ and is then connected to the spring, causing the spring to stretch. If the spring %3D %3D stretches by 1.0 cm, find the required density of the gas mixture, and find how much helium and air you need to produce that mixture.
topic Formalas momantun/energy P=mv/KE :Y2mv*/PE, smg h 2 momentun lenergy PE, - Yikx*/ '½mv°-kE/P=mū Roy Kine Mmatús 3 momentun /anegy Fr -MF/ KE-Yemv/p:uv/ W=Fd co9 4 pressure 5 density / buoyancy S=V=|Z F-mi l F=8Vg 6 densty/buoyanca S| Fg=3 V Z E e má A= Y4nd? 3 B
Transcribed Image Text:topic Formalas momantun/energy P=mv/KE :Y2mv*/PE, smg h 2 momentun lenergy PE, - Yikx*/ '½mv°-kE/P=mū Roy Kine Mmatús 3 momentun /anegy Fr -MF/ KE-Yemv/p:uv/ W=Fd co9 4 pressure 5 density / buoyancy S=V=|Z F-mi l F=8Vg 6 densty/buoyanca S| Fg=3 V Z E e má A= Y4nd? 3 B
Expert Solution
Step 1

Given:

Spring constant K=90.0N/m

Mass of balloon and gas mixture is m=2.50g=2.50*10-3kg.

Density of  mixture of helium is ρh=0.179kg/m3

Density of air is ρair=1.29 kg/m3

Volume V=4.00m3

x=1.0cm=0.01m

Step 2

The total weight is balanced by restoring force

Mg=kx

Where, M=m+mb

(m+mb)g=kx

m+mb=kxg.....(1)

Where, mb is a mass of balloon.

mb=ρv.....(2)

Plugging equation(2) in equation (1)

m+ρV=kxg

ρV=kxg-m

ρ=kxg-mV

Plugging all given values in above formula

We get,

ρ=90*0.019.8-2.50*10-34

ρ=0.022 kg/m3

Thus the required density of gas mixture is 0.022kg/m3

 

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