Loop-the-Loop Motion Laboratory Simulation

Loop evidenceLive observation

Release the cart and watch its speed and track contact around the loop.

Speed0.00 m/s

Normal force0.0 N

Height0.00 m

Track stateAt release

Loop-the-Loop LaboratoryPaused

ModeStudent

How can a cart complete a loop?

It must keep enough speed at the top for a curved path. Release height supplies energy; the track pushes inward only while contact remains possible.

Release from a chosen height.
Watch speed and inward force around the circle.
Test whether the cart stays on the track.

Coaster controls

Sound

Release height2.7 R

Loop radius1.00 m

Cart mass2.0 kg

Track loss coefficient0.00

Simulation speed1×

Live analysis

Top speed needed3.13 m/s

Ideal minimum height2.50 m

Released energy53.0 J

Loop positionRamp

View and cart focus

Drag to pan. Tap the cart, top, or loop center for a short explanation.

Energy history

Teacher demonstrations

Guided visual lecture

Chapter 1 of 80%

Ready. The opening ten seconds define loop-the-loop motion visually.

Language

Narrator

Playback speed1×

Embedded narration plays through this tab for external screen recording.

1. The vertical loop

Watch: The cart leaves the ramp and circles the loop.

Chapters

Loop-the-loop equations

Inward acceleration: a_c = v²/R

Force at the bottom: N = m(v²/R + g)

Force at the top: N = m(v²/R − g)

Minimum top speed: v_top = √(gR)

Ideal minimum release height: h = 2.5R, measured from the bottom for a point-like cart released from rest.

Ideal energy: mgh = 1/2 mv² + mgy

The optional loss setting represents energy lost per distance along the track. A real cart's wheels, axle, and track geometry can change the threshold.

Learning objectives

Explain why speed is needed at the top.
Show velocity tangent to the track and acceleration inward.
Compare normal force at bottom and top.
Use energy and contact conditions together.

Suggested investigations

Try 2.5R with zero loss, then 2.4R.
Increase loss and observe where contact breaks.
Double the radius and compare the required top speed.
Change mass and compare the contact threshold.

Questions for exploration

Why can the normal force be zero at the top?
What happens just after the cart leaves the track?
Why does mass cancel from the ideal height ratio?

Teacher whiteboard

Use a finger, stylus, mouse, Android device, or smart board. Ten full-size pages keep their own drawings.

Pen color

Line width4

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Knowledge check

Seven questions0 / 7

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