Balancing the beam

The idea

A lever, such as the beam of a balance, is balanced when effort × effort arm = load × load arm.

The seesaw

A heavy child sits close to the middle of a seesaw. A lighter child sits far from the middle. The seesaw can be level.

What do you think decides whether a seesaw is level?

• Both the weights and the distances from the middle
• Who is heavier
• Who sits farther

Balance the beam

The load is 60 N and 2 m from the fulcrum (an example). Set the effort and its arm.

Force times arm

When the effort was 60 N at 2 m, 30 N at 4 m, or 20 N at 6 m, the beam balanced. In each case effort × effort arm equalled load × load arm, 120 N m. A smaller effort balanced the same load when it was placed farther from the fulcrum.

A lever, such as the beam of a balance, is balanced when effort × effort arm = load × load arm.

Notes

A lever is balanced when effort × effort arm = load × load arm.

Check yourself

A load of 60 N is 2 m from the fulcrum. An effort of 30 N balances it. How far from the fulcrum is the effort, in m?

Answer: 4 m

30 N × a = 60 N × 2 m = 120 N m, so a = 4 m.

A child of 15 kg sits 2 m from the fulcrum of a seesaw. A child of 30 kg should sit how far from the fulcrum to balance it, in m?

Answer: 1 m

15 kg × 2 m = 30 kg × L, so L = 1 m.

Which condition balances a lever?

An effort of 20 N is placed 6 m from the fulcrum. What load at 2 m from the fulcrum does it balance?

• Effort × effort arm = load × load arm — correct. Yes!
• Effort + effort arm = load + load arm. The balance condition is a product, not a sum.
• Effort = load, whatever the arms. The arms matter. A smaller effort can balance a larger load if its arm is longer.
• 20 N. Solve 20 × 6 = load × 2. The load is 60 N, not 20 N.
• 60 N — correct. Yes!
• 40 N. Solve 20 × 6 = load × 2, which gives 120 ÷ 2 = 60 N.