Apply Pressure = Force / Area
Scenario
Aapke paas ek `5 kg` ki eent (brick) hai. Agar aap isko sidha khada karke table pe rakhte hain to ek nishaan padd jata hai, lekin flat rakhne par nahi.
Formula se kaise saabit (prove) karein ki same eent ka asar uski position par depend karta hai?
Mental model
Formula as a balancer: Upar rakho force (weight) aur usko divide kar do area se.
`Pressure = Force / Area`. Numerator mein force (Newton) hai aur denominator mein area (`meter²`). Ek object apna alag-alag area zameen pe dikha sakta hai, isliye uska `P` bhi badalta rahega, jabki `F` (uske weight) same hai.
Explanation
Pressure ka formula `P = F / A`, numericals solve karne ka main tool hai. Yahan `F` thrust ya force hai jo perpendicular direction mein lag raha hai, aur `A` woh area hai jo surface ke contact mein hai.
Problem solve karte waqt do cheezon ka dhyan sabse zyada rakhna padta hai. Pehli, unit conversion. Bahut baar area `cm²` ya `mm²` mein diya hota hai. Pascal (`Pa`) use karne ke liye aapko Area hamesha `m²` (square meters) mein convert karna hoga. (Yaad rakhein `1 cm² = 10^-4 m²`).
Doosri baat `F` (force) nikalna. Kai baar `F` direct nahi diya hota, balki object ka mass diya hota hai. Aise cases mein force uska weight hota hai, isliye hum pehle `W = m × g` se `F` nikalte hain. Uske baad area se divide karke pressure calculate karte hain.
Jaise ek wooden block (dimensions `20 × 10 × 5 cm`) table par rakha ho. Agar aap use uske `20 × 10 cm` wale face par rakhenge toh area sabse bada hoga aur pressure sabse kam. Agar `10 × 5 cm` wale face par rakhenge toh area sabse chhota hoga aur pressure sabse zyada.
Worked example
Problem: A block of mass `5 kg` and dimensions `20 cm × 10 cm × 5 cm` is placed on a table with its `20 cm × 10 cm` face in contact with the table. Find the pressure exerted on the table. (Take `g = 9.8 m/s^2`)
- Pehle thrust ya force nikalenge `W = m * g` lagakar.
- Ab area of contact calculate karte hain jo `20 cm × 10 cm` hai. Ise meter mein convert karna hoga.
- Ab formula mein rakh kar divide karenge.
Answer: `2450 Pa`
Problem: A woman weighing `500 N` stands on one foot. The area of contact of her stiletto heel with the ground is `0.0001 m^2`. Calculate the pressure exerted on the ground.
- Force seedha diya gaya hai kyunki weight `500 N` hai.
- Area pehle se hi square meters mein hai.
- Formula `Pressure = Force / Area` lagayenge.
Answer: `5,000,000 Pa`
Key points
- Area Conversion is MUST: Always convert `cm` or `mm` to meters before calculating area, or properly adjust the final area unit.
- Force is Weight: Do not divide mass directly. First convert mass to force (weight) by multiplying by acceleration due to gravity (`9.8 m/s²`).
Common mistakes
- Forgetting to square the conversion factor: Bache `100 cm = 1 m` jante hain, aur wo `cm²` ko `m²` banate waqt sirf `100` se divide karte hain. Actually unhe `100 × 100` yani `10000` se divide karna hota hai.
Recall questions
- If a force of `100 N` is applied over an area of `2 m²`, what is the pressure?
- What happens to pressure if the force is doubled over the same area?
- Why do school bags have wide straps?
Questions & answers
A girl of mass `40 kg` stands on one foot. The area of her foot is `100 cm^2`. What is the pressure she exerts on the ground? (`g = 10 m/s^2`)
`40,000 Pa`.
Approach: Force = `40 * 10 = 400 N`. Area = `100 cm^2 = 100 / 10000 m^2 = 0.01 m^2`. Pressure = `400 / 0.01 = 40000 Pa`.
Calculate the pressure if a force of `100 N` acts on an area of `2 m²`.
`50 Pa`
Approach: Pressure = `Force / Area = 100 / 2 = 50 Pa`.
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