IB Physics SLTopic A.3 — Work, Energy & PowerPaper 1 & 2Mechanical Energy Conservation~7 min read
Mechanical Energy Conservation
Kinetic, gravitational potential and elastic potential energy are three sides of the same coin — together they make up an object’s mechanical energy. When nothing dissipates it, that total stays fixed even as it flows between the three.
📘 What you need to know
Mechanical energy is the sum of kinetic, gravitational potential and elastic potential energy
Where there are no resistive forces, the total mechanical energy of a system stays constant
A non-conservative force — like friction or air resistance — removes energy from the system as it does work
Common examples include a swinging pendulum, an object in freefall, and a skier descending a slope
Any change in total mechanical energy equals the work done by or against a non-conservative force
What Is Mechanical Energy?
Mechanical energy bundles together the three stores you’ve already met in this topic.
Mechanical energy
Mechanical energy = Ek + ΔEp + EH
Mechanical Energy in an Oscillating Spring-Mass System
A mass hanging from a vertical spring is a great way to see all three stores in action at once. As the mass moves up and down, energy shifts continuously between kinetic, gravitational potential and elastic potential — but the total never changes.
As the mass oscillates, energy is exchanged between gravitational, kinetic and elastic stores — the total mechanical energy stays the same throughout
Position A (highest point): the mass is momentarily at rest, so kinetic energy is zero, while gravitational PE is at its maximum for the oscillation
Position B (equilibrium): the mass moves at its fastest, so kinetic energy is at its maximum, with gravitational and elastic PE both at intermediate values
Position C (lowest point): the mass is momentarily at rest again, so kinetic energy is zero, while elastic PE is at its maximum because the spring is stretched the most
For a horizontal mass-spring system, gravitational PE doesn’t come into it at all, since height never changes — energy simply swaps between kinetic and elastic stores.
The Conservation Principle
Provided there are no resistive, frictional forces acting, the total mechanical energy of a system is conserved — it stays exactly the same throughout the motion, even though the split between kinetic, gravitational and elastic stores keeps changing.
This shows up in plenty of familiar situations:
a pendulum swinging back and forth
an object in freefall
a skier or skateboarder descending a slope
In the absence of resistive forces
Loss in gravitational potential energy = Gain in kinetic energy
If elastic PE is involved instead — say, a mass on a horizontal spring — the same idea applies:
Loss in elastic potential energy = Gain in kinetic energy
When a non-conservative force, such as friction, does act, the change in total mechanical energy is equal to the work done by that force. This is really just conservation of energy again, expressed for a system that isn’t perfectly isolated from resistive effects.
🧭 Recipe: Solving a Mechanical Energy Conservation Problem
Identify the stores involved — decide which of kinetic, gravitational PE and elastic PE are changing
Check for resistive forces — note whether friction or air resistance is stated, and how much energy it removes
Write the conservation equation — “loss = gain” if nothing is dissipated, or with a dissipated term included if it is
Substitute and solve — swap in mgh, ½mv², ½k(Δx)² as needed, then rearrange for the unknown
Quick recap: Mechanical energy = KE + GPE + EPE. With no resistive forces, this total stays fixed — energy just moves between the three stores.
WE 1
A pendulum bob of mass 0.40 kg is released from rest at a height of 0.18 m above its lowest point. Assuming air resistance is negligible, calculate its speed at the lowest point of the swing.
Step 1 — Apply conservation of mechanical energy
Loss in gravitational PE = Gain in kinetic energy
mgh = ½mv²Step 2 — Cancel mass and rearrange for vv = √(2gh) = √(2 × 9.8 × 0.18)≈ 1.9 m s⁻¹
WE 2
A skier descends 240 m along a slope inclined at 28° to the horizontal, starting from rest. Air resistance and friction dissipate 15% of the gravitational PE lost. Calculate the skier’s final speed.
Step 1 — Find the vertical height droppedh = 240 × sin(28°) ≈ 112.7 mStep 2 — Only 85% of the GPE lost becomes kinetic energy½mv² = 0.85 × mghStep 3 — Cancel mass and rearrange for vv = √(0.85 × 2 × 9.8 × 112.7)≈ 43 m s⁻¹ (2 s.f.)
💡 Top tips
Mass usually cancels out in these problems — don’t panic if a question doesn’t give you one
Always check whether the question mentions friction or air resistance before assuming energy is perfectly conserved
“Work done” in these problems means the same thing as “energy transferred” — the two phrases describe the same process
Sketch the system and label which store is maximum at each point before writing any equations
⚠ Common mistakes
Assuming mechanical energy is always conserved, even when a question explicitly mentions dissipation
Forgetting to convert a percentage dissipated into the correct fraction remaining (e.g. 15% lost means 85% remains)
Including gravitational PE in a purely horizontal spring-mass system, where height never changes
Mixing up which store is at its maximum at each position in an oscillation
Up next: Energy & Power — where we bring time into the picture and see how quickly energy gets transferred.
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