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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
Mode

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.

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

Coaster controls

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.

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: ac = v²/R

Force at the bottom: N = m(v²/R + g)

Force at the top: N = m(v²/R − g)

Minimum top speed: vtop = √(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.

Knowledge check

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