Collection · 4 games

Force equilibrium: when everything cancels

An object in equilibrium stays at rest because the forces on it, and their turning effects, cancel. These games, from two topics, all use it: play them to balance vectors, size cables, place weights on a lever, and share a load between supports.

The two conditions for equilibrium

An object at rest stays at rest only if the vector sum of the forces on it is zero, ΣF = 0: split into components, ΣFₓ = 0 and ΣF_y = 0, and drawn head to tail the forces close into a polygon. It also must not start turning, so the moments about any point cancel, ΣM = 0, where each moment is a force times its perpendicular distance, M = F·d. Forces that all act at one point only need the first condition; a plank, a lever, or a bridge needs both.

Force balance
ΣF = 0
Torque balance
ΣM = 0

Games in this collection

4 games

PLAY NOW · 19

Force Table: Balance the Ring

Balance a ring pulled by strings at different angles. Discover why 3 N and 4 N need exactly 5 N to cancel, and why only the vector sum matters.

Vector sumEquilibrium
Play Force Table
Equilibrium
ΣF = 0
Sizes
|F₁ + F₂| ≤ |F₁| + |F₂|

PLAY NOW · 32

Hanging Sign: Balance the Cables

Hang a 20 kg sign from one or two cables. Use ΣF = 0 to find each tension, discover why flat cables pull much harder, and find the shallowest angle a cable can take.

Force equilibriumTension
Play Hanging Sign
Up and down
Σ T·sin θ = W
Across
T₁·cos θ₁ = T₂·cos θ₂

PLAY NOW · 33

Seesaw: Balance the Torques

Balance a seesaw with children of different masses. Use torque, weight × distance, to place them, include the plank's own weight, and find the force that lifts a wheelbarrow.

TorqueRotational equilibrium
Play Seesaw
Balance
ΣM = 0
Torque
M = m·g·d

PLAY NOW · 34

Plank Bridge: Share the Load

Load a plank resting on two supports. Use ΣF = 0 and ΣM = 0 to find each support's reaction, include the plank's weight, and find where a support cracks or the plank tips.

Static equilibriumSupport reactions
Play Plank Bridge
Forces
R_A + R_B = W + w
Moments about A
R_B·L = W·x + w·x_c

How each game uses it

  1. Force table Three strings pull a ring at different angles. Find the force that makes the vector sum zero, so the ring stays centred.
  2. Hanging sign A sign hangs from one or two cables. Split each tension into components with ΣF = 0 to find how strong each cable must be.
  3. Seesaw Children sit at different distances from the pivot. Balance the torques with ΣM = 0, including the plank's own weight.
  4. Plank bridge A plank rests on two supports. Use ΣF = 0 and ΣM = 0 together to find each reaction, and where a support cracks or the plank tips.

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