Apply potential energy formula
Scenario
Aapko ek 10 kg ka bag ground floor se 3rd floor par le jana hai. Lift kharab hai.
Bag ki height aur mass se aap kaise pata lagaoge ki upar le jaane mein exact kitni energy store hogi?
Mental model
Jitna bhaari object (m), jitni strong gravity (g) aur jitni zyada height (h), utni zyada energy.
Gravitational potential energy seedhe mass, gravity aur height ke multiple ke barabar hoti hai. Formula Ep = m g h ban jata hai kyunki Work = Force × Distance = (mg) × h.
Explanation
Kisi m mass ke object ko h height tak uthane ke liye hume minimum force chahiye hoga uske weight ke barabar, yaani `m × g` (jahan `g` acceleration due to gravity hai, approx `9.8 m/s^2` ya sometimes questions mein `10 m/s^2`).
Ab Work done ka formula hum jaante hain `W = Force × displacement`. Yahan force hai `mg` aur vertical displacement hai height `h`. Toh work done ho gaya `W = mg × h = mgh`. Kyunki yahi work energy banke store hota hai, isliye Gravitational Potential Energy ka formula hota hai `Ep = mgh`.
Ek aur bahut interesting cheez: potential energy sirf is baat par depend karti hai ki shuru mein object kahan tha aur end mein kahan pucha. Rasta (path) chahe jo bhi ho—chahe aap object ko sidhiyan (stairs) se le jao, ya seedhe rassi (rope) se khinch lo—agar initial aur final vertical heights same hain, toh gain in potential energy same rahegi (`mgh`). Ise path independence kehte hain.
Worked example
Problem: A rooftop water tank contains 500 kg of water. The tank is located 15 meters above the ground. Calculate the potential energy stored in this water. (Use g = 9.8 m/s^2)
- Sabse pehle, pani ka mass, height aur gravity ki value note karo.
- Potential energy ka formula apply karo.
- Values multiply karke final energy nikal lo. Yeh wahi energy hai jo pani ko neeche pipes mein pressure se flow karati hai.
Answer: 73500 J
Problem: An object of mass 12 kg is at a certain height above the ground. If the potential energy of the object is 480 J, find the height at which the object is with respect to the ground. Given, g = 10 m/s^2.
- Is baar energy di hui hai aur height nikalni hai.
- Formula likho mgh ka.
- Values ko equation mein put karo.
- 120 ko dusri side bhej kar divide karo height h nikalne ke liye.
Answer: 4 m
Key points
- Formula for Potential Energy: Ep = mgh, where m is mass, g is acceleration due to gravity, and h is height.
- Path Independence: Work done against gravity depends only on the difference in vertical heights, not on the path taken.
Common mistakes
- Using incorrect g value: Agar question mein g = 10 diya hai, toh usko 10 hi use karo calculation aasan banane ke liye. Agar kuch nahi diya, toh by default 9.8 m/s^2 use karna safe rehta hai.
Recall questions
- What is the formula for gravitational potential energy?
- If height is halved, what happens to the gravitational potential energy?
- What does 'g' stand for in the formula Ep = mgh?
Questions & answers
A mass of 10 kg is at a point A on a table. It is moved to a point B. If the line joining A and B is horizontal, what is the work done on the object by the gravitational force?
Zero.
Approach: Since the line is horizontal, there is no change in height (h = 0). Vertical displacement is zero, so work done by gravity is zero. Path independence also supports this.
A 5 kg mass is raised to a height of 2 m. Calculate the potential energy. (g = 9.8 m/s^2)
98 J.
Approach: PE = mgh = 5 * 9.8 * 2 = 98 J.
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