Why does changing the mass not change the speed?

Gravity mg, the normal force and friction μN are all proportional to the mass, so the mass cancels in Newton’s second law. The acceleration depends only on g, the track shape and μ, so the speed is the same and every energy simply scales with m. Air drag breaks this: the drag force c·v² does not depend on mass, so the deceleration c·v²/m is smaller for a heavier rider, who ends up faster.

What does it take to get round a loop?

At the top of the loop the required centripetal force mv²/R must be at least the weight mg, so the normal force N = m(v²/R − g) ≥ 0, i.e. v ≥ √(gR) at the top. Without friction, energy conservation then says the start must be at least 2.5R above the bottom of the loop. The tool shows the normal force live; when it reaches zero the ball falls away.

Why is energy lost when the ball lands back on the track?

On landing, the component of velocity normal to the track is absorbed (a perfectly inelastic impact) and only the tangential component survives. The kinetic energy ½m·v_n² of that normal component becomes thermal energy (sound, deformation, heat), so the thermal bar jumps while the total stays constant. Real ski-jump landing hills are steep precisely to keep that normal component small.

Does it matter where I put the zero of potential energy?

Not physically. Only differences in mgh matter; moving the zero adds the same constant to the potential energy everywhere, and to the total, but the kinetic energy, speed and motion are unchanged. With the zero below the ball PE is positive; above it PE is negative and the pie chart shows only the positive parts.

How accurate is the simulation?

On the track the state is the arc length s and speed v, integrated with fourth-order Runge–Kutta at 0.5 ms steps, with the dissipated energy integrated alongside. On the frictionless presets the total energy stays within 0.01% over 20 seconds.

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🛹Energy Skate Park - Kinetic & Potential Energy, Friction, Energy Bar Charts

A ball rides along a smooth track you can reshape, while bar and pie charts of kinetic, potential and thermal energy update live. When the normal force drops to zero the ball flies off as a projectile and, on landing, the normal part of its kinetic energy turns into heat. Add friction and air drag to watch mechanical energy drain away, drag the zero level of potential energy, and change the mass and gravity (Earth, Moon, Mars, Jupiter).

Free · No sign-up · Runs in your browserLast updated: 2026-10-29

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How to use Energy Skate Park

1Pick a preset track (U-ramp, double well, loop, ski jump, roller coaster), or tick "Edit track" and drag the control points
2Drag the ball onto the track and let go to start it rolling, or drop it in mid-air
3Adjust mass, friction, air drag and gravity, and watch the energy bars, pie chart and speed
4Read the energy–position graph: the gap between the potential curve and the mechanical-energy line is the KE, and where they meet are the turning points

FAQ

Why does changing the mass not change the speed?: Gravity mg, the normal force and friction μN are all proportional to the mass, so the mass cancels in Newton’s second law. The acceleration depends only on g, the track shape and μ, so the speed is the same and every energy simply scales with m. Air drag breaks this: the drag force c·v² does not depend on mass, so the deceleration c·v²/m is smaller for a heavier rider, who ends up faster.
What does it take to get round a loop?: At the top of the loop the required centripetal force mv²/R must be at least the weight mg, so the normal force N = m(v²/R − g) ≥ 0, i.e. v ≥ √(gR) at the top. Without friction, energy conservation then says the start must be at least 2.5R above the bottom of the loop. The tool shows the normal force live; when it reaches zero the ball falls away.
Why is energy lost when the ball lands back on the track?: On landing, the component of velocity normal to the track is absorbed (a perfectly inelastic impact) and only the tangential component survives. The kinetic energy ½m·v_n² of that normal component becomes thermal energy (sound, deformation, heat), so the thermal bar jumps while the total stays constant. Real ski-jump landing hills are steep precisely to keep that normal component small.
Does it matter where I put the zero of potential energy?: Not physically. Only differences in mgh matter; moving the zero adds the same constant to the potential energy everywhere, and to the total, but the kinetic energy, speed and motion are unchanged. With the zero below the ball PE is positive; above it PE is negative and the pie chart shows only the positive parts.
How accurate is the simulation?: On the track the state is the arc length s and speed v, integrated with fourth-order Runge–Kutta at 0.5 ms steps, with the dissipated energy integrated alongside. On the frictionless presets the total energy stays within 0.01% over 20 seconds.

Features

Parametric cubic spline track with continuous curvature and a live normal force
Leaves the track when N < 0 and loses energy on landing; optional coaster mode keeps the wheels locked on
Kinetic, potential, thermal and total energy as bars and a pie, plus energy–position and energy–time graphs
Draggable zero level of potential energy
Mass slider showing that speed does not depend on mass without drag
RK4 integration at 0.5 ms steps with energy error below 0.01%

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