Work and Energy
Work, Kinetic & Potential Energy, Power
In-Text Questions (Page 148)
Q1. A force of 7 N acts on an object. The displacement is, say 8 m, in the direction of the force. Let us take it that the force acts on the object through the displacement. What is the work done in this case?
Formula: Work (W) = Force (F) × Displacement (s)
Calculation: W = 7 N × 8 m = 56 J.
In-Text Questions (Page 149)
Q1. When do we say that work is done?
Work is said to be done when a force acts on an object and the object covers a distance in the direction of the force.
Q2. Write an expression for the work done when a force is acting on an object in the direction of its displacement.
W = F × s, where W is work done, F is force, and s is displacement.
In-Text Questions (Page 152)
Q1. What is the kinetic energy of an object?
Kinetic energy is the energy possessed by an object due to its motion. Moving water, wind, and a moving car all possess kinetic energy.
Q3. The kinetic energy of an object of mass m moving with a velocity of 5 m/s is 25 J. What will be its kinetic energy when its velocity is doubled? What will be its kinetic energy when its velocity is increased three times?
Principle: Ek ∝ v². If velocity becomes n times, K.E. becomes n² times.
K.E. becomes 2² = 4 times. New K.E. = 25 × 4 = 100 J.
K.E. becomes 3² = 9 times. New K.E. = 25 × 9 = 225 J.
In-Text Questions (Page 156)
Q1. What is power?
Power is the rate of doing work or the rate of transfer of energy.
Power = Work / Time
Q3. A lamp consumes 1000 J of electrical energy in 10 s. What is its power?
P = W / t
P = 1000 J / 10 s = 100
W.
Main Textbook Exercises
Q4. Certain force acting on a 20 kg mass changes its velocity from 5 m/s to 2 m/s. Calculate the work done by the force.
Work-Energy Theorem: Work done = Change in Kinetic Energy.
K.E.initial = ½mu² = 0.5 × 20 × (5)² = 250 J.
K.E.final = ½mv² = 0.5 × 20 × (2)² = 40 J.
Work = 40 - 250 = -210 J (Negative sign means work done opposes motion).
Q10. An object of mass 40 kg is raised to a height of 5 m above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.
(i) Potential Energy (at top): Ep = mgh = 40 × 10 × 5 = 2000 J. (Taking g=10 m/s²)
(ii) Half-way down: At half height, half of the
Potential Energy is converted to Kinetic Energy.
K.E. = 2000 / 2 = 1000 J.
Q14. An electric heater is rated 1500 W. How much energy does it use in 10 hours?
Power = 1500 W = 1.5 kW. Time = 10 h.
Energy = Power × Time = 1.5 kW × 10 h = 15 kWh (or 15 Units).
Work and Energy
Work, Power & Conservation Laws
1. Conditions for Work Done
Force and Displacement are in the same direction (θ = 0°). W = +Fs.
Example: A horse pulling a cart.Force and Displacement are in opposite directions (θ = 180°). W = -Fs.
Example: Frictional force acting on a moving car.Force is perpendicular to Displacement (θ = 90°), or Displacement is zero.
Example: A coolie carrying a load and walking on level ground (Force of gravity is down, motion is forward).2. Forms of Energy
Energy due to motion.
Energy due to position/shape.
3. Law of Conservation of Energy
Energy can neither be created nor be destroyed; it can only be transformed from one form to another. Total energy remains constant.
For a freely falling body.
4. Power & Commercial Unit
Power: Rate of doing work. SI Unit: Watt (W).
1 kilowatt (kW) = 1000 W.
Commercial Unit: kilowatt-hour (kWh) or 'Unit'.
Relation: 1 kWh = 3.6 × 106 Joules.
5. Numerical Examples
A porter lifts a luggage of 15 kg from the ground and puts it on his head 1.5 m above the ground. Calculate work done by him.
Force required = Weight = mg = 15 × 10 = 150 N.
Work = F × s = 150 × 1.5 = 225 J.
A 60 W bulb is used for 6 hours daily. Calculate the 'units' of energy consumed in a day.
Energy = Power (kW) × Time (h) = (60/1000) × 6 = 0.06 × 6 = 0.36 Units.
Key Facts & Definitions
50+ Important Points to Remember
Product of force and displacement in direction of force (W = F × s).
SI unit of Work (and Energy). 1 J = 1 Nm.
Capacity to do work. Scalar quantity.
Energy possessed by a body due to its motion (½mv²).
Energy possessed by a body due to its position or configuration (mgh).
Work done in raising an object against gravity.
Energy can neither be created nor destroyed, only transformed.
Sum of Kinetic Energy and Potential Energy.
Rate of doing work (Work/Time).
SI Unit of Power. 1 J/s.
1000 Watts.
kilowatt-hour (kWh).
3.6 × 10⁶ J.
When displacement is zero or force is perpendicular to displacement.
Force and displacement in same direction (θ < 90°).
Force and displacement in opposite direction (θ > 90°).
Energy stored in a stretched or compressed spring/bow.
Energy stored in chemical bonds (e.g., food, battery).
Ratio of useful power output to total power input.
Another unit of power. 1 hp = 746 Watts.
Ultimate source of energy for Earth.
Process converting solar energy into chemical energy.
Work done by net force = Change in Kinetic Energy.
Potential energy decreases, Kinetic energy increases.
Continuous interconversion between KE and PE.
1 kWh.
Force can exist without work (pushing a wall), Work needs force.
Work and Energy do not have direction.
Always negative (wipes out kinetic energy).
W = mgh (depends only on vertical height, not path).
1,000,000 Joules.
Total energy consumed / Total time taken.
Depends on mass and velocity². Velocity has greater impact.
Depends on mass and height.
Possesses Potential Energy.
Possesses both Kinetic and Potential Energy.
Potential Energy.
Kinetic Energy.
Energy stored in muscles (Chemical energy source).
Converts electrical energy to mechanical energy.
Converts mechanical energy to electrical energy.
Converts light energy to electrical energy.
Converts electrical energy to sound energy.
Converts sound energy to electrical energy.
Converts chemical energy to electrical energy.
Converts electrical energy to light (and heat) energy.
Work done against friction appears as heat energy.
Studied nature of heat and mechanical work. Unit named after him.
Power = Force × Velocity (Instantaneous power).
Scarcity of energy resources. Need for conservation.