When a labourer moves a loaded cart, the work done is calculated using the formula W = F × d × cosθ, where F is the applied force, d is the displacement, and θ is the angle between the force and the direction of motion. If the force is applied horizontally and displacement is horizontal, maximum work is done (θ = 0°, W = Fd). If the force is perpendicular to displacement, work done is zero.
Work done = F × d × cosθ, where θ is the angle between force and displacement.
If force is parallel to displacement (θ = 0°), work done is maximum: W = Fd.
If force is perpendicular to displacement (θ = 90°), work done is zero.
A porter carrying a load horizontally does zero work on the load (force is vertical, displacement is horizontal).
SI unit of work is the joule (J); 1 J = 1 N × 1 m.
Net work done = change in kinetic energy (work-energy theorem).
Work done against friction is converted to heat energy.
Work done by a force: W = F · d = F × d × cosθ
Where:
Special cases:
Example: A labourer pushes a cart with 100 N over 20 m horizontally. W = 100 × 20 × cos0° = 2000 J
While a labourer pushes a cart on a level road:
Net work done = Work by applied force − Work against friction = Fd − fd = (F − f) × d
By Work-Energy Theorem: Net work = ΔKE = ½mv² − ½mu²
If cart moves at constant speed: Net work = 0, so F = f (applied force = friction)
An important case: A porter (labourer) carrying a load on the head while walking horizontally.
This is a classic example of zero work in physics. The porter does no work in the physics sense on the load, even though they feel tired (their muscles are doing internal biological work).
Note: Work is done against gravity only when the load is lifted vertically.
Work done = F × d × cosθ, where F is the applied force, d is the displacement, and θ is the angle between force and displacement. For a horizontal push on a level road (θ = 0°), W = F × d.
Zero work is done on the load. The force applied by the labourer is vertical (upward), while the displacement is horizontal. Since the angle between force and displacement is 90°, W = F × d × cos90° = 0.
Work done against friction = friction force × displacement = f × d = μmg × d, where μ is the coefficient of friction, m is the mass, and g is gravitational acceleration. This work is dissipated as heat.
Work done = F × d × cosθ = 200 × 15 × cos0° = 200 × 15 × 1 = 3000 J (3 kJ), assuming the force is applied horizontally in the direction of motion.
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