Motion on a Frictionless Inclined Plane

See how gravity’s components create motion without friction.

Ready

Drag to rotate ramp • Shift-drag to pan • wheel or pinch to zoom • tap cart to track

How to use

1Choose case

2Set angle

3Predict

4Release

Mode

Examples

Ramp & cart controls

Ramp angle30°

Cart mass5.0 kg

Gravity9.81 m/s²

Ramp length12 m

Initial velocity0.0 m/s

Run & 3D camera

Simulation speed1×

View rotation0°

Camera height48°

Zoom1.00×

Live concept explanation

Ready to release

Gravity points straight down. Only its component parallel to the ramp changes the cart’s motion.

Down-ramp acceleration = gravity × sine of ramp angle. Mass does not appear.

Measurements

Acceleration

4.91 m/s²

Velocity

0.00 m/s

Normal force

42.5 N

Time

0.00 s

Motion & energy graph

velocitykinetic energypotential energy

Cart focus

No cart selectedFree camera

Ramp position: —Height: —Total energy: —Net force: —

Teacher / investigation tools

Start positionComparison massPrediction timeGravity preset

Learning objectives

Resolve weight into components parallel and perpendicular to a ramp.
Explain why acceleration on a frictionless incline is independent of mass.
Relate ramp angle to acceleration and normal force.
Track conversion between gravitational potential and kinetic energy.
Predict downhill motion and an uphill launch followed by reversal.

Forces on the cart

Weight points vertically downward. The ramp’s normal force points perpendicular to its surface. With no friction, there is no force opposing motion along the ramp.

Down-ramp weight component = mass × gravity × sine of angle
Into-ramp weight component = mass × gravity × cosine of angle
Normal force = mass × gravity × cosine of angle
Acceleration = gravity × sine of angle

Common misconception: a heavier cart has a larger downhill force, but it also has proportionally more inertia. These effects cancel, so carts of different mass have the same acceleration on the same frictionless ramp.

Energy story

At the top, the cart has maximum gravitational potential energy. As it descends, potential energy decreases while kinetic energy increases. With no friction, their sum stays constant.

A steeper ramp gives greater acceleration.
For the same vertical drop, final speed does not depend on the ramp angle.
The steeper ramp reaches the bottom sooner because the path has a larger downhill acceleration.
An uphill-moving cart slows because acceleration still points downhill.

Guided investigations

1. Angle and acceleration

Set the angle to 15 degrees and record acceleration.
Try 30, 45, and 60 degrees.
Compare the down-slope force arrow.
Explain why acceleration approaches gravity as the ramp becomes vertical.

2. Mass independence

Select Two different masses.
Release both carts together.
Observe that their positions and velocities match.
Compare their forces and energies, which do depend on mass.

3. Earth versus Moon

Keep angle and length fixed.
Compare Earth and Moon gravity.
Record acceleration and travel time.
Explain the differences using the gravity control.

Questions for exploration

At what angle is the normal force largest?
Why does the normal force not make the cart speed up?
Can velocity point uphill while acceleration points downhill?
Which quantities change with mass and which do not?
How can two ramps with different angles give the same final speed?