Work due to Gravity - Physics

1. Fundamental Concepts

Definition: Work due to gravity is the work done by the force of gravity on an object as it moves through a distance.
Formula: The work \(W\) done by gravity can be calculated using the formula \(W = m \cdot g \cdot h\), where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity, and \(h\) is the vertical displacement.
Units: Work is measured in joules (J) in the International System of Units (SI).

2. Key Concepts

Gravitational Force: \(F = m \cdot g\)

Work Calculation: \(W = F \cdot d \cdot \cos(\theta)\)

Where \(F\) is the force applied, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement.

Application: Used to calculate energy changes in systems involving gravitational forces.

3. Examples

Example 1 (Basic)

Problem: Calculate the work done by gravity when a 5 kg object is lifted vertically upward by 10 meters.

Step-by-Step Solution:

Identify the values: \(m = 5 \text{ kg}\), \(g = 9.8 \text{ m/s}^2\), \(h = 10 \text{ m}\).
Calculate the work: \(W = m \cdot g \cdot h = 5 \cdot 9.8 \cdot 10\).
Simplify: \(W = 490 \text{ J}\).

Validation: Substitute values into the formula \(W = m \cdot g \cdot h\). Original calculation matches simplified result: \(490 \text{ J}\).

Example 2 (Intermediate)

Problem: A 2 kg object slides down a frictionless incline that makes a 30-degree angle with the horizontal. If the object slides 5 meters along the incline, calculate the work done by gravity.

Step-by-Step Solution:

Identify the values: \(m = 2 \text{ kg}\), \(g = 9.8 \text{ m/s}^2\), \(d = 5 \text{ m}\), \(\theta = 30^\circ\).
Calculate the vertical displacement: \(h = d \cdot \sin(30^\circ) = 5 \cdot \frac{1}{2} = 2.5 \text{ m}\).
Calculate the work: \(W = m \cdot g \cdot h = 2 \cdot 9.8 \cdot 2.5\).
Simplify: \(W = 49 \text{ J}\).

Validation: Substitute values into the formula \(W = m \cdot g \cdot h\). Original calculation matches simplified result: \(49 \text{ J}\).

4. Problem-Solving Techniques

Visual Strategy: Draw diagrams to visualize the forces and displacements involved.
Error-Proofing: Always check units and ensure they are consistent throughout the problem.
Concept Reinforcement: Understand the relationship between force, displacement, and the angle between them.