Conservation of energy, explained.
Gravity transfers energy from potential to kinetic form as height decreases. On a frictionless ramp, total mechanical energy stays constant. A steeper ramp changes acceleration and travel time, but the speed at the bottom depends only on the vertical drop.
The relationship to remember
Key formulas
- Gravitational potential energy
- PE = mgh
- h measured from a chosen reference level
- Kinetic energy
- KE = ½mv²
- Never negative
- Conservation of mechanical energy
- PE₀ + KE₀ = PE + KE
- No friction or drag
- Speed after a drop from rest
- v = √(2gΔh)
- Mass cancels
- Acceleration along the ramp
- a = g sin θ
- Sets the travel time, not the final speed
Worked example
Problem. A 2 kg block starts from rest 5 m above the bottom of a frictionless ramp. Find its kinetic energy and speed halfway down (2.5 m high) and at the bottom.
- Total mechanical energy: mgh₀ = 2 × 9.81 × 5 = 98.1 J.
- Halfway down: PE = 2 × 9.81 × 2.5 = 49.05 J, so KE = 98.1 − 49.05 = 49.05 J.
- Speed halfway: v = √(2KE/m) = √(2 × 49.05 / 2) = 7.00 m/s.
- At the bottom all 98.1 J is kinetic: v = √(2 × 9.81 × 5) = 9.90 m/s.
Answer. Halfway down the block has 49.05 J of kinetic energy and moves at 7.00 m/s; at the bottom it reaches 9.90 m/s.
A quick check
Dropping through 5 m gives a final speed of √(2 × 9.81 × 5) ≈ 9.90 m/s, regardless of mass in this model.
Inside the default experiment
- Total energy = mgh₀ = 2 × 9.81 × 5 = 98.1 J.
- At height 4.69 m, potential energy = 91.97 J. Kinetic energy = 98.1 − 91.97 = 6.13 J.
- Speed = √(2g(h₀ − h)) = 2.48 m/s. Travel time to the bottom = 2.02 s.
When this model applies
A sliding point mass starts from rest. No friction, air drag, or rotational energy; g = 9.81 m/s².
Make a prediction. Then test it.
Change the ramp angle but keep its height. Does the final speed change?
Try it: Conservation of energy on a ramp ↗Frequently asked questions
Wondering about the why? Start here.
Why does mass not affect the final speed?
Equating mgh to ½mv² lets mass cancel. Both available potential energy and required kinetic energy grow in proportion to mass.
Where does the energy go if there is friction?
Some mechanical energy is transferred into thermal energy and other forms. This experiment deliberately excludes those losses.