Work

Definition: Work is the measure of energy transfer when a force acts on an object and causes it to move in the direction of the force. Mathematically, it is represented as the dot product of force (F) and displacement (d):

W=Force ⋅ displacement

W=F.d

Keep this in mind that work is only done if there is a change in position. If you stay at the same place and read 50 books for an exam, its still not work according to physics.

Key Points:

• No Work: When the force is perpendicular to the displacement, or if there’s no displacement, no work is done (W = 0) because the force does not contribute to moving the object in the direction of the displacement.

Imagine pushing a box across a floor. If you push the box horizontally, it moves in that direction, and you’re doing work. However, if you push the box downward while it’s moving horizontally, you’re just pressing it against the floor without making it move any faster or further in the direction it’s already going. In this case, your downward push (force) doesn’t help with the horizontal movement (displacement). Thus, no work is done by the perpendicular force.

• Units: The unit of work is the joule (J), and it is a scalar quantity (it only has magnitude and no direction). One joule is equal to one newton-metre (1 J = 1 N⋅m). It means one Newton of force was used to move the object through a displacement of 1 metre.

Analogy: Consider pushing a shopping cart:

• Positive Work: Pushing it in the direction you want to go.

• Negative Work: Pushing it backward.

• No Work: Holding it still without moving.

Relationship between work and energy

Work and energy are closely related concepts in physics. Here’s how they are connected:

1. Work as a Transfer of Energy:

   • When work is done on an object, energy is transferred to or from that object. For instance, when you lift a book, you are doing work against gravity, and this work transfers energy to the book, increasing its gravitational potential energy.

2. Work-Energy Theorem:

   • The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. This means if you apply a force to move an object, the energy used to move it (work) changes the object’s energy (like speeding it up or slowing it down).

3. Types of Energy:

   • Work can transfer energy in various forms, such as kinetic energy (energy of motion), potential energy (stored energy due to position), thermal energy (heat), and more. For example, when you push a sled up a hill, you are converting your muscular energy (chemical energy) into the sled’s gravitational potential energy.

4. Conservation of Energy:

   • The principle of conservation of energy states that energy cannot be created or destroyed, only transferred or converted from one form to another. When work is done, it transforms energy from one form to another. For example, in a car engine, the chemical energy in fuel is converted to kinetic energy (motion) through the work done by the engine.

Mathematically, Work done can also be represented as the change in energy (ΔE) of an object:

Example: 

• Lifting a book : picking it from the ground to put it on a shelf will Increase the book’s gravitational potential energy.

• Dropping the Book: Gravity does work on it, converting potential energy into kinetic energy.

Energy Conversion: The Work-Energy Principle

Definition: The work-energy principle states that the work done on an object is directly related to the change in its energy.

Key Points:

• Energy Forms: Energy can exist in forms like kinetic energy, potential energy, and chemical energy.

• Energy Transformation: Work done on an object can change one or more of these energy forms.

Analogy: Think of energy as water flowing through a system of pipes:

• Adding Water (Work Done): Increases the water level (energy) in a reservoir (object).

• Releasing Water: Decreases the water level, representing energy loss or transformation.

Practical Examples

1. Lifting Objects:

   • Scenario: Lifting a 10 kg box to a height of 2 meters.

   • Calculation: 

2. Pushing a Cart:

   • Scenario: Pushing a cart with a force of 50 N for a distance of 5 meters.

   • Calculation: 

Rules for Measuring Work:

1. Direction of Force and Displacement:

   • Work is maximised when the force is applied in the direction of displacement.

   • No work is done if the force is perpendicular to the displacement.

2. Consistency in Units:

   • Ensure that force is measured in newtons (N) and displacement in metres (m) for the work to be in joules (J).

3. Scalar Quantity:

   • Work is a scalar quantity and does not have direction, only magnitude.