Work and Energy

Discover the fascinating world of energy - from kinetic and potential energy to the universal law of energy conservation!

โ˜€๏ธ
๐Ÿ’จ
Wind Energy
๐Ÿ’ง
Hydro Energy
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Fossil Fuels
๐ŸŒฑ
Plants
โš›๏ธ
Nuclear
๐ŸŒ‹
Geothermal
Slow Object
KE = 0 J
Fast Object
KE = 0 J
Kinetic Energy
Work Done
Displacement: 0 cm
Energy Transfer
Trolley KE
โ†’
Block KE

Activity 10.7 Controls

Hanging Mass: 100 g
Question 1: Work Done by Force
A force of 7 N acts on an object. The displacement is 8 m in the direction of the force (Fig. 10.3). Let us take it that the force acts on the object through the displacement. What is the work done in this case?
๐Ÿ“ฆ โ†7N โ€”โ€”โ€”โ€”8mโ€”โ€”โ€”โ€” ๐Ÿ“ฆ
Fig. 10.3: Force acting in direction of displacement
Solution:
Given:
Force, F = 7 N
Displacement, s = 8 m
Direction: Force and displacement are in the same direction
Formula:
W = F ร— s ร— cos ฮธ
Since force and displacement are in the same direction, ฮธ = 0ยฐ
Therefore, cos ฮธ = cos 0ยฐ = 1
Calculation:
W = F ร— s
W = 7 N ร— 8 m
W = 56 J
The work done is 56 J (Joules)
Example 10.4: Work-Energy Theorem
What is the work to be done to increase the velocity of a car from 30 km hโปยน to 60 km hโปยน if the mass of the car is 1500 kg?
๐Ÿš— 30 km/h โ†’ ๐Ÿš— 60 km/h
Car accelerating from 30 to 60 km/h
Solution:
Given:
Mass of car, m = 1500 kg
Initial velocity, u = 30 km hโปยน
Final velocity, v = 60 km hโปยน
Convert to m/s:
u = 30 ร— (1000/3600) = 25/3 m sโปยน
v = 60 ร— (1000/3600) = 50/3 m sโปยน
Apply Work-Energy Theorem:
W = ฮ”KE = KEf - KEi
KEi = ยฝ ร— 1500 ร— (25/3)ยฒ = 156,250/3 J
KEf = ยฝ ร— 1500 ร— (50/3)ยฒ = 625,000/3 J
W = 625,000/3 - 156,250/3
W = 468,750/3 = 156,250 J
Work done = 156,250 J = 156.25 kJ
Example 10.6: Potential Energy
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 sโปยฒ.
๐Ÿ“ฆ โ† h = ?
โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”โ€”
๐ŸŒ Ground Level
Object at height h above ground
Solution:
Given:
Mass of object, m = 12 kg
Potential energy, PE = 480 J
Acceleration due to gravity, g = 10 m sโปยฒ
Height, h = ? (to find)
Formula:
PE = mgh
Rearranging for height:
PE = mgh
480 J = 12 kg ร— 10 m sโปยฒ ร— h
480 = 120 ร— h
h = 480/120 = 4 m
The object is at a height of 4 m above the ground
h = 2m
PE = 196 J
h = 3m
PE = 294 J
h = 4m
PE = 392 J

Energy Conservation

Kinetic
Potential
Total
Kinetic Energy
KE = ยฝmvยฒ
Energy possessed by an object due to its motion. It depends on both mass (m) and velocity (v). Notice that velocity is squared, so doubling speed increases kinetic energy by 4 times!
Potential Energy
PE = mgh
Energy possessed by an object due to its position or height. It depends on mass (m), acceleration due to gravity (g), and height (h) above reference level.
Conservation of Energy
KE + PE = Constant
Total mechanical energy remains constant in the absence of friction. As one form decreases, the other increases by the same amount, keeping the total energy unchanged.
Work-Energy Theorem
W = ฮ”KE
Work done on an object equals the change in its kinetic energy. This fundamental relationship connects the concepts of work and energy in physics.
๐Ÿš€ Kinetic Energy Calculator
Enter values to calculate kinetic energy
โ›ฐ๏ธ Potential Energy Calculator
Enter values to calculate potential energy
Explore Work and Energy
What is Energy?
Energy is the capacity to do work. An object having a capability to do work is said to possess energy. The object which does the work loses energy and the object on which the work is done gains energy. Energy is measured in Joules (J), the same unit as work.
Energy = Capacity to do Work
๐Ÿš€
Kinetic Energy
Energy due to motion. Faster objects have more kinetic energy.
โ›ฐ๏ธ
Potential Energy
Energy due to position or height. Higher objects have more potential energy.
๐Ÿ”ฅ
Heat Energy
Energy due to temperature. Hot objects have more heat energy.
๐Ÿ’ก
Light Energy
Energy carried by light waves. Brighter light has more energy.
โšก
Electrical Energy
Energy due to moving electric charges. Powers our devices.
๐Ÿงช
Chemical Energy
Energy stored in chemical bonds. Found in food and fuel.
Activity 10.6: Ball Drop Experiment
  • Take a heavy ball and drop it on a thick bed of sand
  • Drop the ball from different heights: 25 cm, 50 cm, 1m, and 1.5m
  • Observe the depth of depressions made at each height
  • Notice that greater height creates deeper depression
  • This shows that objects at greater heights have more energy
Activity 10.7: Trolley and Block Experiment (NCERT)
  • Set up the apparatus as shown in Fig. 10.5 with trolley, wooden block, and pulley system
  • Place a wooden block of known mass in front of the trolley at a fixed distance
  • Place a known mass on the pan so that the trolley starts moving
  • The trolley moves forward and hits the wooden block, which gets displaced
  • Note down the displacement of the block - this means work is done on the block
  • From where does this energy come? (Answer: From the kinetic energy of the moving trolley)
  • Repeat by increasing the mass on the pan - greater mass = more displacement = more work done
  • Conclusion: Moving objects possess kinetic energy and can do work
Law of Conservation of Energy
Energy can neither be created nor destroyed; it can only be converted from one form to another. The total energy of an isolated system remains constant. This is one of the most fundamental laws of physics.
Total Energy = Constant
NCERT Example 10.3: Kinetic Energy Calculation
  • Problem: Find kinetic energy of 15 kg object moving at 4 m/s
  • Given: m = 15 kg, v = 4 m/s
  • Formula: KE = ยฝmvยฒ
  • Solution: KE = ยฝ ร— 15 ร— 4ยฒ = ยฝ ร— 15 ร— 16 = 120 J
  • Answer: The kinetic energy is 120 J
NCERT Example 10.5: Potential Energy Calculation
  • Problem: Find potential energy of 10 kg object at 6 m height
  • Given: m = 10 kg, h = 6 m, g = 9.8 m/sยฒ
  • Formula: PE = mgh
  • Solution: PE = 10 ร— 9.8 ร— 6 = 588 J
  • Answer: The potential energy is 588 J