Simple machines.

Step 1 of 7

Less force

The block and tackle in the Scene hangs the load on four runs of rope, and each run carries an equal share of it. Your hand pulls only one run. The load divided by the effort is the machine’s mechanical advantage. With the load $F_1$⁠ and the effort $F_2$⁠, the mechanical advantage is $\dfrac{F_1}{F_2}$⁠.

Here the mechanical advantage is $4$⁠, the number of rope runs holding the load.

Step 2 of 7

The price: distance

As the load rises, each of the four runs gets shorter by the same amount. All that rope comes out at the free end, in your hand. Predict how far you have to pull, then choose Forces under Show the forces and see the brackets that measure the two distances.

Step 3 of 7

The work does not change

The force is four times smaller, and the distance four times bigger. The work you do, the effort times its distance, equals the work the machine does on the load, the load times the height it rises:

$F_2 \cdot d_2 = F_1 \cdot d_1$$F_2 \cdot d_2 =$$F_1 \cdot d_1$⁠

Here $d_1$⁠ is how far the load rises and $d_2$⁠ how far your hand pulls.

A machine can trade force for distance, but it cannot save work. If it gave out more work than was put in, it would be making energy from nothing.

Step 4 of 7

The lever

In a lever, a bar that turns about a fulcrum, the rule looks different. A force acting far from the fulcrum turns the bar harder than the same force close to it. A force times its distance from the fulcrum is its moment, and the lever balances when the moments on the two sides are equal:

$F_1 \cdot d_1 = F_2 \cdot d_2$$F_1 \cdot d_1 =$$F_2 \cdot d_2$⁠

Here $d_1$⁠ and $d_2$⁠ are the distances from the fulcrum, the arms. The effort’s arm is three times as long, so the mechanical advantage is $3$⁠. As the lever turns, the long end also moves three times as far: the same work on both sides.

Step 5 of 7

Choosing a machine

Each of the three machines can give any mechanical advantage from $1$⁠ to $4$⁠. Choose what you need with Machine and the other controls.

Step 6 of 7

Efficiency

A real machine loses part of the work put into it: friction in the axles warms them, and the pulleys themselves have to be lifted too. The efficiency of a machine is the share of the work that reaches the load: the work the machine does on the load, $W_1$⁠, divided by the work put into it, $W_2$⁠:

$\eta = \frac{W_1}{W_2}$$\eta =$$\frac{W_1}{W_2}$⁠

For an ideal machine, like the ones in the Scene, the efficiency is $100\%$⁠. For a real machine it is always less.

Step 7 of 7

In summary

• The mechanical advantage is the load divided by the effort. In a block and tackle it is the number of rope runs holding the load, and in a lever the ratio of the arms.
• What you save in force you pay in distance: in an ideal machine the work in equals the work out.
• Efficiency is the work out divided by the work in. In a real machine it is less than $100\%$⁠, and the rest becomes heat.