WORK AND ENERGY
Chapter 10, 'Work and Energy', introduces fundamental concepts in physics crucial for understanding how the world functions. Students learn the scientific definition of work, distinguishing it from everyday usage, and explore various forms of energy, including kinetic and potential energy. The chapter also delves into the law of conservation of energy and the concept of power, which measures the rate of doing work. Mastering these topics is essential for building a strong foundation in physics.
Work (कार्य)
Work ek fundamental concept hai physics mein. Daily life mein hum 'work' ka matlab kuch aur samajhte hain, but science mein iski ek specific definition hai.
Scientific Conception of Work
Work done tabhi mana jaata hai jab do conditions fulfill hon:
- Force (बल) act kare: Object par koi force lagna chahiye.
- Displacement (विस्थापन) ho: Object force ki direction mein move karna chahiye.
Agar inmein se koi bhi condition satisfy nahi hoti, toh scientific terms mein work done zero hota hai.
- Example: Agar aap ek deewar ko dhakka de rahe ho aur woh move nahi karti, toh aapne koi work nahi kiya, bhale hi aap thak gaye ho.
Work Done by a Constant Force
Jab ek constant force \(F\) kisi object par act karta hai aur object \(s\) distance displace hota hai force ki direction mein, toh work done \(W\) hota hai:
- Formula: \(W = F \times s\)
- \(F\) = Magnitude of Force
- \(s\) = Displacement in the direction of force
Units of Work
- SI Unit: Joule (J)
- \(1\text{ Joule}\) = \(1\text{ Newton} \times 1\text{ metre}\)
- Definition of 1 Joule: \(1\text{ J}\) woh work done hai jab \(1\text{ N}\) ka force kisi object ko \(1\text{ m}\) displace karta hai force ki direction mein.
Types of Work Done
Work done positive, negative ya zero ho sakta hai, depending on the angle between force aur displacement.
- Positive Work: Jab force aur displacement same direction mein hon. \(\theta = 0^\circ\).
- Example: Ek ball ko neeche fekna. Gravity ka force aur ball ka displacement dono neeche ki taraf hain.
- \(W = Fs\)
- Negative Work: Jab force aur displacement opposite direction mein hon. \(\theta = 180^\circ\).
- Example: Ek object ko upar uthana. Aapka force upar hai, but gravity ka force neeche hai. Gravity negative work kar rahi hai.
- \(W = -Fs\)
- Zero Work: Jab force aur displacement ke beech ka angle \(90^\circ\) ho, ya jab displacement zero ho, ya jab force zero ho.
- Examples:
- Ek porter apne sir par load lekar horizontal platform par chal raha hai. Gravity ka force neeche hai, displacement horizontal hai. Angle \(90^\circ\). Work done by gravity = 0.
- Ek satellite earth ke around circular orbit mein ghoom raha hai. Centripetal force towards center hai, displacement tangential hai. Angle \(90^\circ\). Work done by centripetal force = 0.
- Deewar ko dhakka dena (displacement zero).
- Object par koi force na lagna (force zero, e.g., uniform velocity).
Work as a Scalar Quantity
Work ki sirf magnitude hoti hai, direction nahi. Isliye yeh ek scalar quantity hai.
Work (कार्य): Scientific terms mein, work tabhi hota hai jab ek force kisi object par act kare aur us object mein force ki direction mein displacement ho.
Work Done: \(W = F \times s\)
Where:
- \(W\) = Work Done (Joule)
- \(F\) = Force (Newton)
- \(s\) = Displacement (metre)
Yaad rakho, agar question mein 'work done by gravity' pucha hai aur object ko upar uthaya ja raha hai, toh answer negative hoga. Agar object neeche aa raha hai, toh positive.
Energy (ऊर्जा)
Energy is the capacity to do work. Jab koi object work karta hai, toh woh energy lose karta hai, aur jis object par work hota hai, woh energy gain karta hai.
Units of Energy
- SI Unit: Joule (J) (same as work)
- \(1\text{ Joule}\) = \(1\text{ Newton} \times 1\text{ metre}\)
- Larger Unit: kilojoule (kJ)
- \(1\text{ kJ} = 1000\text{ J}\)
Forms of Energy
Energy ke bahut saare forms hote hain, jaise:
- Mechanical Energy: Kinetic Energy + Potential Energy
- Heat Energy
- Chemical Energy
- Electrical Energy
- Light Energy
- Sound Energy
- Nuclear Energy
Kinetic Energy (गतिज ऊर्जा)
- Energy possessed by an object due to its motion.
- Jitni zyada speed, utni zyada kinetic energy.
- Derivation of Kinetic Energy Formula:
- Consider an object of mass \(m\) moving with initial velocity \(u\).
- A constant force \(F\) acts on it, displacing it by \(s\) and changing its velocity to \(v\).
- Work done \(W = F \times s\).
- From Newton's Second Law: \(F = ma\).
- From Third Equation of Motion: \(v^2 - u^2 = 2as \implies s = \frac{v^2 - u^2}{2a}\).
- Substitute \(F\) and \(s\) in work done equation:
\(W = (ma) \times \left(\frac{v^2 - u^2}{2a}\right)\) \(W = \frac{1}{2}m(v^2 - u^2)\)
- Agar object rest se start karta hai, toh \(u=0\).
- Toh, \(W = \frac{1}{2}mv^2\).
- This work done is stored as kinetic energy.
- Formula: \(E_k = \frac{1}{2}mv^2\)
- \(E_k\) = Kinetic Energy (Joule)
- \(m\) = Mass of the object (kg)
- \(v\) = Velocity of the object (m/s)
Potential Energy (स्थितिज ऊर्जा)
- Energy possessed by an object due to its position or configuration.
- Gravitational Potential Energy: Jab kisi object ko height par uthaya jaata hai, toh usmein gravitational potential energy store ho jaati hai.
- Derivation of Gravitational Potential Energy Formula:
- Consider an object of mass \(m\) raised to a height \(h\) from the ground.
- Minimum force required to raise the object = Weight of the object = \(mg\).
- Work done against gravity \(W = \text{Force} \times \text{Displacement} = mg \times h = mgh\).
- This work done is stored as gravitational potential energy.
- Formula: \(E_p = mgh\)
- \(E_p\) = Potential Energy (Joule)
- \(m\) = Mass of the object (kg)
- \(g\) = Acceleration due to gravity (\(9.8\text{ m/s}^2\) or \(10\text{ m/s}^2\))
- \(h\) = Height (metre)
- Elastic Potential Energy: Stretched rubber band ya compressed spring mein stored energy. Yeh uski configuration change hone ki wajah se hoti hai.
Law of Conservation of Energy (ऊर्जा संरक्षण का नियम)
- Energy can neither be created nor destroyed; it can only be transformed from one form to another.
- Total energy of an isolated system always remains constant.
- Example: Free falling object.
- Top (height \(h\)): \(E_p = mgh\), \(E_k = 0\) (velocity = 0). Total Energy = \(mgh\).
- Mid-way: \(E_p\) decreases, \(E_k\) increases. \(E_p + E_k = \text{constant}\).
- Just before hitting ground (height = 0): \(E_p = 0\), \(E_k = \frac{1}{2}mv^2\) (maximum velocity). Total Energy = \(\frac{1}{2}mv^2\).
- Throughout the fall, \(E_p + E_k = \text{Constant} = \text{Mechanical Energy}\).
- Air resistance ko ignore kiya jaata hai is law ko apply karte waqt simple cases mein.
Energy (ऊर्जा): The capacity of an object to do work. Iski unit Joule (J) hai.
Kinetic Energy: \(E_k = \frac{1}{2}mv^2\)
Potential Energy: \(E_p = mgh\)
Potential energy ki value reference level par depend karti hai. Ground level ko generally zero potential energy level mana jaata hai.
Law of Conservation of Energy states ki energy ko na toh banaya ja sakta hai aur na hi destroy kiya ja sakta hai, bas ek form se doosre form mein convert kiya ja sakta hai. Total energy hamesha constant rehti hai.
Rate of Doing Work (Power) (शक्ति)
Power batata hai ki work kitni tezi ya dheere se kiya ja raha hai, ya energy kitni tezi se transfer ho rahi hai.
Definition of Power
- Power is the rate of doing work or the rate of transfer of energy.
- Formula: \(P = \frac{W}{t}\)
- \(P\) = Power (Watt)
- \(W\) = Work Done (Joule)
- \(t\) = Time taken (seconds)
- Alternatively, agar energy transfer ho rahi hai, toh \(P = \frac{E}{t}\).
Units of Power
- SI Unit: Watt (W) (James Watt ke samman mein)
- Definition of 1 Watt: \(1\text{ Watt}\) woh power hai jab \(1\text{ Joule}\) work \(1\text{ second}\) mein kiya jaata hai.
- \(1\text{ W} = 1\text{ J/s}\)
- Larger Units:
- Kilowatt (kW): \(1\text{ kW} = 1000\text{ W}\)
- Horsepower (hp): \(1\text{ hp} \approx 746\text{ W}\) (commonly used for motors and engines)
Commercial Unit of Energy
- Electricity bills mein energy ko kilowatt-hour (kWh) mein measure kiya jaata hai.
- \(1\text{ kWh}\) = Energy consumed by an appliance of \(1\text{ kW}\) power in \(1\text{ hour}\).
- Conversion to Joules:
\(1\text{ kWh} = 1\text{ kW} \times 1\text{ h}\) \(1\text{ kWh} = (1000\text{ W}) \times (3600\text{ s})\) \(1\text{ kWh} = (1000\text{ J/s}) \times (3600\text{ s})\) \(1\text{ kWh} = 3.6 \times 10^6\text{ J}\)
- \(1\text{ kWh}\) ko commonly 1 unit of electricity bhi kehte hain.
Average Power
- Agar power time ke saath vary karti hai, toh hum average power calculate karte hain.
- Formula: \(\text{Average Power} = \frac{\text{Total Work Done}}{\text{Total Time Taken}}\)
Power (शक्ति): Work karne ki rate ya energy transfer ki rate. Iski SI unit Watt (W) hai.
Power: \(P = \frac{W}{t}\)
Where:
- \(P\) = Power (Watt)
- \(W\) = Work Done (Joule)
- \(t\) = Time taken (seconds)
Commercial unit of energy kilowatt-hour (kWh) hai, jo \(3.6 \times 10^6\text{ J}\) ke barabar hoti hai.
Students aksar Watt (W) ko energy ki unit samajh lete hain, jabki yeh power ki unit hai. Joule (J) energy ki unit hai.
