A.3.7—Mechanical energy conservation

Condition for conservation

Mechanical energy is conserved when only conservative forces transfer energy within the system and friction or other resistive transfers are absent or negligible.

Write the balance

$E_{k,i}+E_{p,i}=E_{k,f}+E_{p,f}$

Choose a convenient zero for potential energy and keep the same reference throughout.

When it is not conserved

Friction, drag or deformation transfer mechanical energy to internal energy. Total energy is still conserved, but the mechanical-energy equation needs an additional transfer term.

How it is assessed

The evidence contrasts a frictionless ramp with a rough surface and includes rolling motion, requiring the correct boundary for mechanical-energy conservation.

Command terms

Calculate / Explain

What earns marks

Use mechanical-energy conservation only over the part of the motion where resistive work is absent or negligible. When the path becomes rough, include the work done by friction or the resulting internal-energy transfer.

Watch for

Applying mechanical-energy conservation across a rough section without subtracting the work done by friction.

Representative question

[Maximum number: 1]

An object is released from rest and slides down a frictionless ramp. The object then leaves the ramp and slides along a rough horizontal surface. The object stops in a distance s along the ramp.

The coefficient of dynamic friction between the object and the rough horizontal surface is $\mu$ .
What is the height of the ramp?

$\mu g s$

$\frac{s}{2 g \mu}$

$\frac{s}{\mu}$

$\mu s$

A.3.7—Mechanical energy conservation

Conserve Mechanical Energy Without Resistive Forces

A.3.7 Exam Analysis

Assessment in practice

Question 1