Top: tension (what the newton meter reads). It peaks every time the bob passes the bottom — twice per period.
Dashed: mg and the predicted peak mg(3 − 2 cos θ₀). Bottom: the angle of the string.
#
object
m / kg
L / m
θ₀ / °
Tmax / N
Tmax/mg
1 − cos θ₀
period / s
How to use this simulation
Choose the object and its size, the string length and the angle θ₀.
Set each value with ▼ and ▲ (hold to go faster; the ↑ ↓ keys or the mouse wheel in the box also work, Shift = ×10), or type a value in the box. ↺ puts it back to its start value. Outside the classroom range the box turns amber ⚠: fine to explore, but the lab can't do this.
Move the pointer over any graph (or tap it): a dashed line shows the values where it cuts each curve, or the values of the nearest data point.
✋ Hold aside: a hand holds the bob still at θ₀ with a horizontal pull. Read the newton meter.
▶ Release: the bob swings. The newton meter reading changes all the time; the Graph tab shows it.
After a few swings press ● Record (peak tension and period).
The physics
Length to the centre of the bob: L = string + r.
Held aside (equilibrium): T cos θ = mg and T sin θ = Fhand ⇒ T = mg / cos θ.
Swinging: along the string the bob moves in a circle, so T − mg cos θ = mv²/L ⇒ T = mg cos θ + mv²/L.
At the bottom (energy: v² = 2gL(1 − cos θ₀)): T = mg(3 − 2 cos θ₀) — independent of L!
Period for small swings: Tperiod = 2π√(L/g) (topic C.1 preview) — independent of m.
Model: air drag ½ρCdAv² (ρ = 1.2 kg m⁻³, Cd = 0.47) slows large light objects; it acts along
the path, so it does not change T directly. The balloon's weight is its rubber (the air inside floats), but the air inside still has to
be moved, which makes it sluggish. Light, inextensible string.
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…).