Foundations — FEEP, MEMS thrusters — micro-propulsion

3.3.43 · D1 · Physics › Rocket Propulsion › FEEP, MEMS thrusters — micro-propulsion

Is page mein assume kiya gaya hai ki aap kuch nahi jaante. Hum parent topic ka har letter build karte hain, ek ek karke, har cheez apni jagah earn karti hai pehle agle se pehle.

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0. Woh picture jis par sab kuch tika hai

Kisi bhi symbol se pehle, woh machine dekho jise hum describe kar rahe hain: ek container mein "stuff" hai aur ek hole hai, aur stuff bahar shoot ho raha hai.

Us picture mein teen cheezein notice karo, kyunki ye hamare pehle teen symbols ban jaate hain:

• har second ek choti mass ka blob nikalta hai,
• woh kisi speed par nikalta hai,
• aur ship ko push feel hoti hai ulti taraf.

Yahi poora subject hai. Ab hum har piece ko naam dete hain.

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1. Mass — symbol $m$

Picture: ek scale par ek lump. Bada lump, bada number.

Topic ko kyun chahiye: ek ion (ek single charged atom) ka mass hota hai — indium ke liye yeh bahut hi chota $m=1.9\times 10^{-25}$ kg hota hai. Jab hum poochte hain "ek ion kitni tez udata hai?", toh jawab is baat par depend karta hai ki woh ion kitna heavy hai: ek heavy ion ko tez phenkna mushkil hai, bilkul waise jaise ek rock phenkna ek pebble se mushkil hai.

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2. Speed aur velocity — symbol $v$ (aur $v_e$)

Picture: ek arrow jiska length speed hai aur jiska point travel ki direction dikhata hai.

Special wala — exhaust velocity $v_e$: chota $e$ bas ek label hai jiska matlab hai "exhaust", yani cheez ki speed jab woh nozzle se nikalti hai. Yeh poore topic mein sabse important number hai. Bada $v_e$ = flag "hum bahut kam fuel use karte hain".

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3. Rate of change — dot, $\dot{m}$

Yahan ek notation aata hai, sirf ek quantity nahi, isliye hum dheere chalte hain.

Picture: ek bucket mein taptapta tap. $m$ hai bucket mein kitna paani hai; $\dot{m}$ hai kitni tez drips jama ho rahi hain — woh flow.

Yeh tool kyun aur sirf $m$ kyun nahi? Thrust ek continuous push hai. Yeh total fuel par depend nahi karta; yeh is baat par depend karta hai ki fuel abhi kitni tez stream ho raha hai. "Per second" ki baat karne ke liye humein ek rate chahiye, aur dot physics mein rate ka shorthand hai. Hum baar baar "kg per second" words mein likh sakte the, lekin dot formulas ko short rakhta hai.

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4. Momentum aur force — symbol $F$

Woh link jis par topic jeeta hai: force hi hai momentum jo har second diya jaata hai. Har second mass $\dot{m}$ phenko, har kg $v_e$ speed carry karta hai, aur jo push aap feel karte ho woh hai

$F=\dot{m}{v}_e.$

Picture: ek skateboard par khado aur baseballs aage phenko — har throw aapko peeche dhakelta hai. Unhe tez phenko ($v_e$ up) ya zyada per second phenko ($\dot{m}$ up), aur aap zyada tez peeche chalte ho ($F$ up).

Topic ko kyun chahiye: yahi literally ek thruster karta hai. $F=\dot{m}{v}_e$ har rocket ka dil hai, bada ho ya micro.

Recall Ek rocket "push" kyun nahi kar sakta empty space ke against?

Woh kuch bhi ke against push nahi karta — woh mass ek taraf phenkta hai aur recoil (Newton ka third law: har push ka ek equal opposite push hota hai) use doosri taraf le jaati hai. ::: Exhaust hi woh cheez hai jiske against woh push karta hai.

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5. Micro-prefixes — $\mu$, m, aur scientific notation

Parent page baar baar "µN" aur "$10^{-25}$" kehta hai. Ye bas size labels hain.

Picture: ek ruler zoom kar raha hai. Ek newton ek seb hai; ek milli-newton ek mosquito landing hai; ek micro-newton ek pollen ka single grain settle ho raha hai. Woh "pollen grain" push exactly woh gentleness hai jo CubeSat attitude control ko chahiye.

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6. Charge aur electric field — $q$, $V$, $E$, ${\epsilon }_0$

FEEP charged atoms ko move karta hai, isliye hum electricity ki language chahiye.

Picture: voltage ek hill hai; charge us par ek ball hai. Steeper/taller hill ($V$ bada) → neeche tez ball.

Topic ko yeh sab kyun chahiye: FEEP ki trick yeh hai ki $E$ ko ek sharp tip par itna enormous bana do ki woh literally charged atoms ko liquid metal se tod ke le aaye aur phir voltage $V$ use karo unhe accelerate karne ke liye. Koi charge nahi, koi grip nahi; koi voltage nahi, koi speed nahi.

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7. Energy conservation — equation $qV=\frac{1}{2}m{v}_e^2$

Yeh parent page par sabse zyada use kiya gaya derivation hai, toh hum isme har symbol earn karte hain.

Idea: energy kabhi lost nahi hoti, sirf convert hoti hai. Ek charge $q$ jo voltage hill $V$ se slide karta hai woh electrical energy $qV$ deta hai. Woh kahan jaati hai? Motion mein. Toh

$\underset{\text{electrical energy spent}}{\underbrace{qV}}=\underset{\text{motion energy gained}}{\underbrace{\frac{1}{2}m{v}_e^2}}.$

AAB HUM KYA KARTE HAIN: speed ke liye solve karo. KYUN: hum $v_e$ chahte hain; equation abhi use ek square ke andar chhupa rahi hai. Square ko square root se undo karo:

$v_e=\sqrt{\frac{2qV}{m}}.$

YEH KAISA DIKHTA HAI: ek heavy ion (neeche bada $m$) dheere niklata hai; bada voltage (upar bada $V$) tez niklata hai — exactly "steeper hill = faster ball" wali picture se match karta hai. Yahi reasoning Ion Thrusters aur Electrospray & Colloid Thrusters ko bhi power karti hai.

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8. Exponential $e^x$ — rocket equation ke liye

Parent ka fuel formula $m_p/m_0=1-e^{-\Delta v/v_e}$ ek ajeeb letter $e$ use karta hai.

Picture: ek hot cup of coffee cool ho rahi hai. Pehle tez girta hai, phir dheere aur dheere, room temperature ki taraf ease karta hai — woh curve hai $e^{-x}$.

Woh magic shortcut jo hum actually use karte hain: jab $x$ tiny hota hai, $e^{-x}\approx 1-x$. Toh ek CubeSat ke liye jahan chahiye speed change $\Delta v$ huge $v_e$ se tiny hai,

$1-e^{-\Delta v/v_e}\approx \frac{\Delta v}{v_e}.$

Isliye "$m_p\approx m_0\Delta v/v_e$" appear hota hai — yeh exponential ka small-$x$ face hai. Poori kahani ke liye dekho Rocket Equation aur Specific Impulse.

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9. Gas symbols — $p$, $T$, $R$, $M$, $\gamma$, $A$, $\rho$, $\mu$

MEMS section ions ko hot gas se replace kar deta hai. Naya cast, same kaam.

Picture: ek shaken fizzy bottle. Andar high pressure aur temperature; cap kholo aur gas bahar rush karta hai, apni stored "push" ko ek fast jet mein convert karta hai — woh hai nozzle jo enthalpy ko $v_e$ mein turn karta hai.

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10. Reynolds number — $Re=\frac{\rho vL}{\mu }$

Parent kehta hai micro-nozzles suffer karte hain kyunki "$Re$ small hai". Yeh iska matlab hai.

Yeh tool kyun aur koi doosra kyun nahi? Engineers ko ek number chahiye predict karne ke liye "kya yeh flow nicely behave karega ya wall friction se bog down ho jaayega?" $Re$ exactly woh number hai. Ek micro-nozzle mein $L$ tiny hai, isliye $Re$ tiny hai — friction dominate karta hai aur ideal-gas formula zyada promise karta hai. Poori kahani: Reynolds Number.

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Prerequisite map

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Equipment checklist

Khud ko test karo — right side cover karo aur reveal karne se pehle jawab do.