Apply power formula
Scenario
Aapke paas do water pumps hain. Dono underground tank se roof tak paani pahuchate hain, par ek 10 minute leta hai aur dusra 2 minute.
Dusre pump ki motor kitni zyada powerful (power rating) hogi, ye aap mathematically kaise bataoge?
Mental model
Dono kaam nikalne hain (mgh) aur fir use time se divide karna hai.
Maximum exam questions mein work directly nahi diya hoga. Aapko pehle lifting ka work (mgh) nikalna padega, aur uske baad P = W/t lagana padega.
Explanation
Pichle concept mein humne Power ka basic formula seekha `P = W/t`. Par direct work (W) ki value exam mein bahut kam questions mein di jati hai. Jyadatar problems real-life situations par based hote hain, jaise ek ladka stairs par chadh raha hai, ya motor paani utha rahi hai.
Jab bhi height involve ho, aapko yaad karna hoga ki work done strictly potential energy mein gaye change ke barabar hota hai, yaani `W = mgh`.
Toh Power ka actual useful formula aisi situations mein ban jata hai: `P = mgh / t`.
Yahan m mass hai (kg mein), g gravity hai (usually 9.8 ya 10 m/s^2), h height hai (meters mein), aur t time in seconds hai. Agar time minutes ya hours mein diya hai, to first step humesha use seconds mein convert karne ka hona chahiye, warna answer ki dhajiya ud jayengi. Uske baad sab multiply aur divide karke answer Watt (W) mein aa jayega.
Worked example
Problem: A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. Take g = 10 m/s^2.
- Pehle mass aur time likh lo.
- Ab total height nikalte hain. 45 steps hain, aur har step 15 cm (0.15 m) ka hai.
- Work done (potential energy gain) nikalo.
- Ab power nikalo work ko time se divide karke.
Answer: 375 W
Problem: An elevator of mass 1000 kg moves upward a distance of 10 m in 20 seconds. What is the power required by the elevator motor? (g = 10 m/s^2)
- Height seedhe 10 m di gayi hai. Work done nikalo.
- Time 20 seconds hai, directly power formula apply karo.
- Calculate karo aur zeroes cancel karo.
Answer: 5000 W
Key points
- Expanded Power Formula: When working against gravity, Power = (mgh) / t.
- Time Conversion: Always ensure time (t) is converted to seconds before calculating.
Common mistakes
- Not converting cm to m: Height agar stairs ki cm mein hai (jaise 15 cm), to students use sidhe multiply kar dete hain. 15 cm ko 0.15 m karna bahut zaroori hai standard units ke liye.
- Not converting minutes to seconds: Agar time 2 minutes diya hai to usko sidhe 2 rakhne se error ayegi. P = W/120 karna hoga, as 1 minute = 60 seconds.
Recall questions
- What formula for power is used when an object is lifted vertically against gravity?
- What is the equivalent of 1 kilowatt (kW) in watts?
- How do you calculate power if you only know energy consumed and time taken?
Questions & answers
A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
100 W
Approach: Directly use P = Energy / time = 1000 / 10.
A boy of mass 50 kg runs up a staircase of 45 steps in 9 s. If the height of each step is 15 cm, find his power. (Take g = 10 m/s^2)
375 W
Approach: Total height h = 45 * 0.15 = 6.75 m. W = mgh = 50 * 10 * 6.75 = 3375 J. P = W/t = 3375 / 9 = 375 W.
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