Calculate Work from Force - Physics

1. Fundamental Concepts

Definition: Work is the energy transferred to or from an object via a force acting on the object in the direction of its displacement.
Formula: The work $W$ done by a constant force $F$ along a displacement $d$ is given by $W = F \cdot d$.
Units: The standard unit of work is the joule (J), where $1 \text{ J} = 1 \text{ N} \cdot 1 \text{ m}$.

2. Key Concepts

Basic Rule: $$W = F \cdot d$$

Directional Component: When the force and displacement are not in the same direction, use the component of force in the direction of displacement: $W = F \cdot d \cdot \cos(\theta)$.

Application: Used to calculate energy transfer in physics problems involving motion and forces.

3. Examples

Example 1 (Basic)

Problem: Calculate the work done by a force of $5 \text{ N}$ that moves an object $10 \text{ m}$ in the same direction.

Step-by-Step Solution:

Identify the force $F = 5 \text{ N}$ and the displacement $d = 10 \text{ m}$.
Apply the formula: $W = F \cdot d = 5 \cdot 10 = 50 \text{ J}$.

Validation: Substitute values into the formula → Original: $5 \cdot 10 = 50$; Simplified: $50 \text{ J}$ ✓

Example 2 (Intermediate)

Problem: A force of $10 \text{ N}$ acts at an angle of $60^\circ$ to the direction of displacement of $5 \text{ m}$. Calculate the work done.

Step-by-Step Solution:

Identify the force $F = 10 \text{ N}$, the displacement $d = 5 \text{ m}$, and the angle $\theta = 60^\circ$.
Calculate the component of force in the direction of displacement: $F \cdot \cos(60^\circ) = 10 \cdot \frac{1}{2} = 5 \text{ N}$.
Apply the formula: $W = F \cdot d \cdot \cos(\theta) = 5 \cdot 5 = 25 \text{ J}$.

Validation: Substitute values into the formula → Original: $10 \cdot 5 \cdot \cos(60^\circ) = 25$; Simplified: $25 \text{ J}$ ✓

4. Problem-Solving Techniques

Visual Strategy: Draw diagrams to represent forces and displacements.
Error-Proofing: Always check the units and ensure they are consistent throughout the calculation.
Concept Reinforcement: Understand the physical meaning of each term in the work formula.