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 the values with the sliders, or type a value in the box next to a slider and press Enter. A value outside the allowed range is set to the nearest allowed value.
✋ 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.