Conservation of energy on a ramp
Slide a block down a frictionless ramp and watch gravitational potential energy turn into kinetic energy while the total stays constant. Conservation of mechanical energy gives mgh₀ = mgh + ½mv², so the speed after a vertical drop Δh is v = √(2gΔh), whatever the mass or the ramp angle.
What if you changed…
Change the ramp angle but keep its height. Does the final speed change?
See the calculation
- 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.
What this model assumes
A sliding point mass starts from rest. No friction, air drag, or rotational energy; g = 9.81 m/s².
Keep an eye on this
A real rolling ball also stores rotational kinetic energy, so this sliding-particle model does not predict its exact speed.
Understand the physics ↗Formulas used in this simulation
- 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
Energy on a ramp: common questions
Wondering about the why? Start here.
How do you find speed from height?
Set the potential energy lost equal to the kinetic energy gained: mgΔh = ½mv². Mass cancels, leaving v = √(2gΔh). A 5 m drop gives about 9.9 m/s.
Does a steeper ramp make the block faster at the bottom?
Not on a frictionless ramp. A steeper ramp gives a larger acceleration, g sin θ, and a shorter trip, but the final speed depends only on the vertical drop.
Is mechanical energy always conserved?
Only when forces such as friction and air resistance do no work. Otherwise some energy is transferred to thermal energy and the final speed is lower.
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.