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Physics · Class 11

Keep a vertical loop taut

Work, Energy & Power

Energy determines how speed changes while the bob climbs. Tension also must remain non-negative because a string cannot push. At the top the minimum taut speed is √(gr), which requires bottom speed √(5gr). A slower bob can turn back or lose string tension before reaching the top; the preview stops at that first limit.

Open the interactive experiment →

Reaching the top is not enough.

கயிறு இழுக்கலாம்; தள்ள முடியாது. மேல்புள்ளியில் கயிறு இறுக்கமாக இருக்க v² ≥ gr தேவை. கீழ்புள்ளியில் குறைந்தபட்ச வேகம் √(5gr).

Key notes, relationships and model limits

Key relationship

v² = vbottom² − 2gr(1 − cosθ); T = m(v²/r + g cosθ). At top: T ≥ 0 ⇒ vtop² ≥ gr ⇒ vbottom² ≥ 5gr.

Remember

Energy determines how speed changes while the bob climbs. Tension also must remain non-negative because a string cannot push. At the top the minimum taut speed is √(gr), which requires bottom speed √(5gr). A slower bob can turn back or lose string tension before reaching the top; the preview stops at that first limit.

Common trap

Energy sufficient to reach top height alone, vbottom² ≥ 4gr, does not ensure a taut full loop.

Model limits

Point bob on a massless inextensible string; constant gravity, no drag. The string can pull but cannot push. The circular preview stops at the first turning point or zero-tension event; free flight after slackening is not modeled.

What you will learn

Combine energy conservation with a unilateral string constraint and find the minimum loop speed.

Try the experiment

Compare just-taut, slack-string and turning presets. Scan the angle and see where continuation stops.

Think of it this way

A flexible leash cannot hold a path that would require it to push the object away.

Worked example

For r = 2 m, critical bottom speed is √98.1 = 9.90 m/s; critical top speed is √19.62 = 4.43 m/s.

Why this matters

Conservation equations must be checked against physical constraints such as non-negative tension.

Before you start

Vector components · velocity · SI units

Check your understanding

The minimum bottom speed for a full vertical loop on an ideal string is…

Read the explanation

Top tension requires vtop² ≥ gr. The climb adds 4gr to the required squared bottom speed, giving 5gr.

Course connection: CBSE XI Chapter 5; NEET/Main Unit 4; JEE Advanced Mechanics. Apply each exam’s stated assumptions.