A longer arm helps

The idea

The mechanical advantage of a lever is load / effort = effort arm / load arm, so increasing the effort arm reduces the effort needed to move the same load.

A long handle

A tight nut is hard to turn with a short spanner but easier with a long one. The long handle puts your hand far from the nut.

What do you think a longer effort arm does for the effort needed?

• It reduces the effort needed
• It increases the effort needed
• It makes no difference

Lengthen the arm

The load is 120 N and its arm is 1 m (examples). Change the effort arm.

The ratio of arms

As the effort arm grew, the effort needed for the same 120 N load fell. The mechanical advantage load ÷ effort came out equal to effort arm ÷ load arm.

The mechanical advantage of a lever is load / effort = effort arm / load arm. So increasing the effort arm reduces the effort needed to move the same load.

Notes

Mechanical advantage of a lever = load / effort = effort arm / load arm. A longer effort arm needs a smaller effort.

Check yourself

A lever has an effort arm of 2 m and a load arm of 0.5 m. What is its mechanical advantage?

Answer: 4

MA = 2 m / 0.5 m = 4.

A lever has a mechanical advantage of 4. What effort moves a load of 100 N, in N?

Answer: 25 N

Effort = 100 N / 4 = 25 N.

The effort arm of a lever is made longer. To move the same load, the effort needed…

The mechanical advantage of a lever is equal to…

• becomes larger. A longer effort arm gives a greater mechanical advantage, so the effort needed is smaller.
• stays the same. The mechanical advantage is the effort arm divided by the load arm, so a longer effort arm lowers the effort needed.
• becomes smaller — correct. Yes!
• effort arm / load arm — correct. Yes!
• load arm / effort arm. That is the inverse. The mechanical advantage is effort arm / load arm.
• effort arm × load arm. It is the ratio of the arms, not their product.