Choose an example at the top: 🧪 lab (a string between two clamp stands) · 🐦 bird on a wire · 🚶 tightrope walker ·
🏮 lantern · 🚦 traffic light · 🪧 sign · 🧺 washing line. The Example list below has more set-ups for each one.
Set the mass m and the angles θL and θR of the threads below the horizontal with ▼ ▲
(hold to go faster; ↑ ↓ keys or the mouse wheel in the box, Shift = ×10) or type a value; ↺ puts it back. Tick
same on both sides for a symmetric set-up. Outside the classroom range the box turns amber ⚠.
Choose the thread: cotton breaks above 20 N, fishing line 100 N, nylon cord 2 kN, steel wire 20 kN.
The mass is held by a hand. Press ▶ Let go. If both threads are strong enough, it hangs at rest. If not, the thread with
the larger tension snaps: the mass swings on the other thread, which may snap too. ◂ / ▸ (or ← →) step through it.
The middle column shows the free-body diagram of the mass, the vector triangle and a table of the components.
Move the pointer over a graph (or tap it) to read values. ● Record saves a trial when the mass hangs at rest;
the Data tab plots T against 1/sin θ (gradient mg/2) and the horizontal and vertical components.
Work through the Tasks tab. Write explanations on your worksheet.
The physics
The mass is at rest, so the resultant force on it is zero: ΣFx = 0 and ΣFy = 0.
Horizontal: TL cos θL = TR cos θR
Vertical: TL sin θL + TR sin θR = mg
Same angle on both sides: 2T sin θ = mg, so T = mg / (2 sin θ).
Only the vertical components hold the mass up. A flat thread (small θ) needs a huge tension, so a loaded thread or wire can
never be perfectly straight. With different angles, the steeper thread has the larger tension.
The three forces drawn tip to tail make a closed vector triangle.
Model: g = 9.81 N kg⁻¹; light threads that do not stretch; supports 4.0 m apart at the same height. After a snap the mass
swings on the other thread (with a little air resistance) or falls freely. The drawings of the objects are not to scale.
Newton's laws
The badge above the scene says which law applies at this moment: 1st law — at rest or moving at a constant velocity, the resultant force is zero (ΣF = 0); 2nd law — accelerating, ΣF = ma. The table under the free-body diagram adds up the forces (ΣF) and compares them with m a (▾ folds it). Tick 3rd-law pairs to see every force with its partner: the same size and type, in the opposite direction, acting on the other body (the Earth, the floor, the string, the fluid…).