Interpret negative work
Scenario
Aap ek bhaagti hui gaadi par brake lagate ho aur gaadi thodi door jaakar ruk jaati hai.
Brakes ke force ne gaadi par kaisa work kiya?
Mental model
Agar koi force aapko rokne ki koshish kar raha hai (jaise friction), toh uska work negative hoga.
Jab force ki direction object ki movement (displacement) ke bilkul opposite hoti hai, toh force effectively uski energy kam kar raha hota hai. Aise force ka work done negative mana jata hai.
Explanation
Work sirf positive ya zero nahi hota, ye negative bhi ho sakta hai. Ye tab hota hai jab force ek object par uski motion ki opposite direction mein lagta hai. Yaani in dono ke beech ka angle 180 degrees hota hai.
Socho agar ek moving car par brakes lagayi jaaye. Brakes jo force apply karti hain, wo car ki motion ko oppose karta hai (piche ki taraf khichta hai), lekin car abhi bhi kuch door aage (forward) move karti hai rukne se pehle. Is case mein displacement aage hai aur force peeche. Aise situations mein hum likhte hain `W = -F s`.
Ek aur common example friction ka hai. Aap ek block ko zameen par aage dhakka dete ho, friction hamesha piche lagti hai motion ko oppose karne ke liye. Toh friction jo work karti hai wo hamesha negative hota hai. Aise hi jab aap kisi object ko zameen se upar uthate ho, aap upward lifting force lagate ho aur motion bhi upward hoti hai (toh aapka work positive hai). Lekin dharti ki gravity to block ko niche kheenchna chahti hai na? Par block toh upar ja raha hai. Isliye, usi same time par gravity ka work negative hota hai.
Worked example
Problem: A car is moving on a straight road. Brakes are applied to stop it. The brakes apply a frictional force of 1000 N, and the car moves 10 m before coming to a complete halt. Find the work done by the brakes.
- Force aur displacement opposite directions mein hain.
- Kyunki direction opposite hai, negative work ka formula use karenge.
- Values put karo.
Answer: -10000 J
Problem: A boy lifts a book of weight 5 N up by 1.5 m. What is the work done by the gravitational force on the book?
- Gravity hamesha niche lagti hai (downward force 5 N), lekin book upar ja rahi hai (displacement 1.5 m up).
- Donon opposite hain, isliye work done by gravity negative hoga.
- Calculate karke answer nikalo.
Answer: -7.5 J
Key points
- Angle of 180 Degrees: Negative work occurs when force and displacement are in exactly opposite directions.
- Formula Modification: For opposite directions, W = -F s.
Common mistakes
- Forgetting the negative sign: Jab question mein 'work done by friction' ya 'work done by gravity (jab object upar ja raha ho)' pucha ho, yaad se negative sign lagana warna answer galat mana jayega.
Recall questions
- When is work done considered negative?
- What is the angle between force and displacement when work done is negative?
- Which force usually does negative work when a block slides on a table?
Questions & answers
An object is thrown vertically upwards and it rises to a height of 10 m. What can you say about the work done by the force of gravity?
The work done by gravity is negative.
Approach: Because gravitational force pulls downward while the object is displaced upward.
When you lift a book from the table, what is the nature of work done by the gravitational force?
The work done by gravity is negative.
Approach: Gravity acts downward, but the book is displaced upward.
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