How to play Hanging Sign
- Choose a sign and read its mass and the cable angles on the card.
- Draw the forces on the ring: the weight down and each tension along its cable. Their sum must be zero.
- Type the tension or the angle and press Hang. The crane hands the weight to the cables over 2 s.
- Watch the force triangle: it closes when the forces balance. A cable rated too low snaps.
When is an object in equilibrium?
An object stays at rest when the forces on it cancel: ΣF = 0. Split every force into horizontal and vertical parts and both sums must be zero. For a sign hanging from two cables at angles θ₁ and θ₂ above the horizontal, the horizontal parts cancel, T₁·cos θ₁ = T₂·cos θ₂, and the vertical parts hold up the weight, T₁·sin θ₁ + T₂·sin θ₂ = W. Drawn head to tail, the three forces make a closed triangle. The flatter a cable, the smaller its vertical part, so it must pull much harder to help hold the same weight: that is why washing lines and power lines are never pulled perfectly straight.
A focused learning model
The cables are light, straight, and do not stretch, and they meet at one ring, so the forces are concurrent. The crane lowers the sign slowly, so the sign is in equilibrium at every moment and the tensions grow in step with the load. A cable snaps exactly when its tension reaches its rating; a rating within 0.05% of the tension counts as holding, so a rounded answer does not snap. Plays in real time.