Given:
Work done, W = Force × Displacement × cosθ
Since force and displacement are in the same direction, θ = 0° and cos0° = 1
Therefore, W = F × s = 7 N × 8 m = 56 J
The work done is 56 Joules.
Work is said to be done when:
Both conditions must be satisfied for work to be done according to the scientific definition.
When force acts in the direction of displacement:
Work done (W) = Force (F) × Displacement (s)
W = F × s
1 joule (1 J) is the amount of work done when a force of 1 newton (1 N) displaces an object by 1 meter (1 m) along the line of action of the force.
1 J = 1 N × 1 m
Force, F = 140 N
Displacement, s = 15 m
Work done, W = F × s = 140 N × 15 m = 2100 J
The work done in ploughing the length of the field is 2100 J.
Kinetic energy is the energy possessed by an object due to its motion. It is the energy an object has because it is moving.
The kinetic energy (Ek) of an object of mass m moving with velocity v is given by:
Ek = ½mv²
Given: Ek = 25 J when v = 5 m/s
We know Ek ∝ v² (since Ek = ½mv² and m is constant)
When velocity is doubled (v = 10 m/s):
New Ek = (2)² × 25 J = 4 × 25 J = 100 J
When velocity is tripled (v = 15 m/s):
New Ek = (3)² × 25 J = 9 × 25 J = 225 J
Power is defined as the rate of doing work or the rate of transfer of energy. It measures how fast or slow work is done.
Power (P) = Work done (W) / Time taken (t)
P = W/t
1 watt is the power of an agent which does work at the rate of 1 joule per second.
1 W = 1 J/s
Energy consumed, W = 1000 J
Time taken, t = 10 s
Power, P = W/t = 1000 J / 10 s = 100 W
The power of the lamp is 100 W.
Average power is obtained by dividing the total energy consumed by the total time taken. It is useful when the power of an agent varies with time.
Average Power = Total energy consumed / Total time taken
Suma is swimming in a pond: Work is done. She applies force to push water backward and moves forward (displacement occurs).
A donkey is carrying a load on its back: No work is done (according to scientific definition) as there is no displacement in the direction of force (force is upward, displacement is horizontal).
A wind-mill is lifting water from a well: Work is done. The wind applies force to lift water against gravity (displacement occurs in the direction of force).
A green plant is carrying out photosynthesis: No work is done (according to scientific definition) as there is no displacement of object.
An engine is pulling a train: Work is done. The engine applies force and the train moves (displacement occurs in the direction of force).
Food grains are getting dried in the sun: No work is done (according to scientific definition) as there is no force causing displacement.
A sailboat is moving due to wind energy: Work is done. Wind applies force on the sail and the boat moves (displacement occurs in the direction of force).
Work done by gravity is zero. This is because the vertical displacement is zero (initial and final points are at the same height), and work done by gravity depends only on vertical displacement, not on the path taken.
Chemical energy (in battery) → Electrical energy (in wires) → Light energy and Heat energy (in bulb)
Mass, m = 20 kg
Initial velocity, u = 5 m/s
Final velocity, v = 2 m/s
Work done = Change in kinetic energy
W = ½mv² - ½mu² = ½m(v² - u²)
W = ½ × 20 × (2² - 5²) = 10 × (4 - 25) = 10 × (-21) = -210 J
The negative sign indicates that work is done against the motion.
Work done by gravitational force is zero. This is because the force of gravity acts vertically downward, while the displacement is horizontal. The angle between force and displacement is 90°, and work done = Fs cosθ = Fs cos90° = Fs × 0 = 0.
No, this does not violate the law of conservation of energy. As the potential energy decreases, the kinetic energy increases by the same amount. The total mechanical energy (potential energy + kinetic energy) remains constant throughout the free fall.
Chemical energy (from food) → Mechanical energy (muscles) → Kinetic energy (bicycle motion) + Heat energy (friction)
No energy transfer occurs to the rock as no work is done on it (no displacement). The energy spent by the person is converted into heat energy in the muscles due to muscular effort and may also cause sweating.
1 unit of energy = 1 kilowatt-hour (kWh)
250 units = 250 kWh
1 kWh = 3.6 × 10⁶ J
250 kWh = 250 × 3.6 × 10⁶ J = 9 × 10⁸ J
Mass, m = 40 kg
Height, h = 5 m
g = 10 m/s²
Potential energy at top, Ep = mgh = 40 × 10 × 5 = 2000 J
At half-way down, height = 2.5 m
Potential energy at half-way = 40 × 10 × 2.5 = 1000 J
By conservation of energy:
Kinetic energy at half-way = Total energy - Potential energy = 2000 - 1000 = 1000 J
Work done by gravity on a satellite moving around the Earth is zero. This is because the gravitational force acts radially toward the center of the Earth, while the displacement of the satellite is tangential (perpendicular to the force). The angle between force and displacement is 90°, so work done = Fs cos90° = 0.
Yes, according to Newton's first law of motion, an object will continue in its state of uniform motion (constant velocity) unless acted upon by an external force. So if an object is already moving with constant velocity, it will continue to move (displacement occurs) even in the absence of any net force.
According to the scientific definition of work, no work is done on the bundle of hay. This is because there is no displacement of the bundle in the direction of the force (the force is applied upward to support the weight, but there is no vertical displacement). The person gets tired due to muscular effort and energy consumption, but no work is done on the hay.
Power, P = 1500 W = 1.5 kW
Time, t = 10 hours
Energy consumed = Power × Time = 1.5 kW × 10 h = 15 kWh
In joules: 15 kWh = 15 × 3.6 × 10⁶ J = 5.4 × 10⁷ J
When a pendulum bob is drawn to one side:
The bob eventually comes to rest due to air resistance and friction at the pivot point, which dissipates energy as heat.
The mechanical energy (potential + kinetic) decreases but the total energy (including heat) remains constant.
This is not a violation of the law of conservation of energy - the energy is transformed, not destroyed.
Work required to bring the object to rest = Change in kinetic energy
Initial kinetic energy = ½mv²
Final kinetic energy = 0 (object at rest)
Work done = 0 - ½mv² = -½mv²
The negative sign indicates work is done against the motion.
Mass, m = 1500 kg
Velocity, v = 60 km/h = 60 × (1000/3600) m/s = 50/3 m/s ≈ 16.67 m/s
Work required = Change in kinetic energy = 0 - ½mv²
W = -½ × 1500 × (50/3)² = -750 × (2500/9) = -750 × 277.78 ≈ -208,333.33 J
The negative sign indicates work is done against the motion. Magnitude of work required is approximately 208,333 J.
Yes, I agree with Soni. When several forces act on an object, if the net force (vector sum of all forces) is zero, then the acceleration will be zero according to Newton's second law (F = ma). This happens when forces are balanced.
Power of one device = 500 W
Power of four devices = 4 × 500 W = 2000 W = 2 kW
Time = 10 hours
Energy consumed = Power × Time = 2 kW × 10 h = 20 kWh
In joules: 20 kWh = 20 × 3.6 × 10⁶ J = 7.2 × 10⁷ J
When a freely falling object hits the ground and stops, its kinetic energy is transformed into other forms of energy such as:
The total energy is conserved, but the kinetic energy is converted to other forms.