Work, Energy, and

Work Done by a Constant Force

Work is a fundamental concept in physics that describes the effect of a force causing displacement of an object. Scientifically, work is said to be done when a force is applied on an object and the object moves in the direction of the applied force. Consider the example of lifting a wheat bag of mass 5 kg from the floor to a height of 1 meter. The gravitational force acting downward on the bag is mg, where m is the mass and g is the acceleration due to gravity. To lift the bag slowly, an upward force equal to mg must be applied. The bag is displaced upward by 1 meter in the direction of the applied force, so work is done. If multiple bags are lifted one after another to the same height, the total work done is proportional to the number of bags. Similarly, lifting a single bag to a greater height increases the work done proportionally. This leads to the scientific definition of work done by a constant force: work done = force applied × displacement in the direction of the force. This definition applies regardless of the direction of force and displacement, whether vertical, horizontal, or any other direction. For instance, if a constant force F acts on an object causing displacement s in the direction of the force, the work done W is W = F × s. It is important to specify both the force doing the work and the object on which work is done. The SI unit of work is the joule (J), where 1 joule equals 1 newton of force causing displacement of 1 meter in the force direction. Mathematically, 1 J = 1 N × 1 m = 1 kg·m²/s². When the force is not constant, the work done can be calculated as the area under the force-displacement graph between initial and final positions. Work done is zero if either the force is zero or the displacement is zero. For example, pushing a rigid wall with no displacement results in zero work done, even though effort is exerted. Similarly, if the force is perpendicular to displacement, such as carrying a box horizontally while applying upward force, the work done by that force is zero. Work done can be positive or negative depending on the relative directions of force and displacement. Positive work occurs when force and displacement are in the same direction, such as pushing a wheelchair forward. Negative work occurs when force and displacement are opposite, such as a goalkeeper applying force opposite to the motion of a ball to stop it. This section lays the foundation for understanding how forces cause energy changes in objects through work.

• Work is done when a force causes displacement in the direction of the force.
• Work done = force × displacement in the direction of force.
• SI unit of work is joule (J), where 1 J = 1 N × 1 m.
• Work is zero if force is zero or displacement is zero.
• Work done can be positive or negative depending on force and displacement directions.
• Work done equals the area under force-displacement graph if force varies.
• 📌 Work: Product of force and displacement in the direction of force.
• 📌 Force: A push or pull acting on an object.
• 📌 Displacement: The distance moved in a specific direction.

The Work-Energy Theorem

The work-energy theorem establishes a fundamental relationship between the work done on an object and the change in its energy. When a force causes displacement, work is done on the object, and this work results in a change in the object's energy. Consider everyday examples such as a fielder throwing a cricket ball towards the wickets or a flowerpot raised to a height and then dropped. The moving ball or falling pot has the capacity to do work on other objects, such as knocking down the wickets or damaging an object below. This capacity to do work is called energy. The ball gains energy from the work done by the fielder in throwing it, and the pot gains energy from the work done in raising it to a height. Positive work done on an object increases its energy, which can later be transferred to other objects through forces causing motion. Mathematically, the work-energy theorem is stated as: work done on an object = change in its energy. This theorem applies even when forces are not constant or when multiple objects interact. It provides a powerful tool to analyze motion and energy changes without detailed force analysis. The SI unit of energy is the joule (J), the same as work. Energy can be transferred not only mechanically but also as heat, radiation, sound, or electrical energy. For example, the Sun's energy reaches Earth as radiation, and energy flows from hot to cold objects as heat. James Prescott Joule, after whom the unit joule is named, studied the relationship between mechanical and thermal energy, establishing the principle of energy conservation. An example in a carrom game demonstrates the work-energy theorem: the striker does positive work on the white coin, increasing its energy; the white coin does negative work on the striker, decreasing its energy; similarly, energy transfers continue through collisions. Understanding the work-energy theorem helps explain many physical phenomena and solve problems involving forces and motion more simply.

• Work done on an object equals the change in its energy (work-energy theorem).
• Energy is the capacity to do work.
• Positive work increases an object's energy; negative work decreases it.
• Energy transfer can occur mechanically, as heat, radiation, or sound.
• The SI unit of energy is the joule (J), same as work.
• James Prescott Joule established the relation between mechanical and thermal energy.
• 📌 Energy: Capacity to do work.
• 📌 Work-energy theorem: Work done on an object equals change in its energy.
• 📌 Positive work: Work done when force and displacement are in the same direction.