Work done (By conservative force – Gravity)

Work Done by a Conservative Force Experiment – For Schools, Teachers, and Students

Definition

Work done by a conservative force refers to the work performed by a force that depends only on the initial and final positions of an object and is independent of the path taken. Examples of conservative forces include:

• Gravitational Force
• Electrostatic Force
• Elastic Spring Force

This concept is demonstrated in Dencity – Online Science Lab and Simulations to enhance interactive learning.

Theory

The work done by a conservative force is associated with a potential energy function. If an object moves from position r₁ to r₂, the work done (W) is:

W = -ΔU = – (U₂ – U₁)

where:

• U₁ and U₂ are the potential energies at the initial and final positions, respectively.
• W is negative if potential energy increases (force opposes motion).
• W is positive if potential energy decreases (force aids motion).

The relationship between force (F) and potential energy (U) is:

F = – ∇U

where -∇U represents the negative gradient of potential energy, meaning the force acts in the direction of decreasing potential energy.

Path Independence in Conservative Forces

For conservative forces, the work done is path-independent and depends only on positions r₁ and r₂:

W = ∫ F · dr

This property allows easy calculation of work using potential energy differences.

Examples of Work Done by Conservative Forces

1. Gravitational Force:
   • For an object of mass m moving vertically under gravity (g):
     W = -ΔU = -mg (h₂ – h₁)
     where h₁ and h₂ are the initial and final heights.
2. Elastic Spring Force:
   • For a spring with constant k, the work done during stretching or compression is:
     W = -ΔU = -(1/2) k (x₂² – x₁²)
     where x₁ and x₂ are the initial and final displacements from equilibrium.

Real-World Applications

The concept of work done by conservative forces is used in:

• Calculating potential energy changes in gravitational or elastic systems.
• Analyzing energy conservation in mechanical systems.
• Modeling motion in gravitational fields and spring-based systems.
• Online Science Lab: Allows students to simulate conservative force work calculations.

Observations and Key Learnings

• Work done by a conservative force depends only on positions, not the path.
• If potential energy increases, work done is negative (force opposes motion).
• If potential energy decreases, work done is positive (force aids motion).
• For a closed path, work done by a conservative force is always zero:∮ F · dr = 0

The Work Done by a Conservative Force Experiment helps students understand how forces like gravity, electrostatics, and elastic springs perform work based only on initial and final positions, regardless of the path taken. This principle is essential in energy conservation and motion analysis.

Using online physics simulations, students can explore how potential energy changes in gravitational and elastic systems. Our interactive teaching tool provide virtual lab experiments, allowing learners to visualize conservative forces in action.

For students looking to complete their science homework, this experiment offers a hands-on way to grasp key physics concepts with practical examples and real-time simulations.