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Around-n-Around: How is a Wheel and Axle Similar to a Lever?

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Author: Janice VanCleave

Problem

How is a wheel and axle similar to a lever?

Materials

• scissors
• box, at least 2 feet (60 cm) tall and 2 feet (60 cm) wide
• broom
• ruler
• string
• book

Procedure

1. Ask an adult to cut two holes across from each other in the sides of the box. The holes should be just slightly larger than the diameter of the broom handle.
2. Push the broom handle through the holes in the box, with the straw part of the broom close to, but not touching, the side of the box.
3. Make a handle by taping a ruler to the end of the broom, as indicated in the diagram.
4. Tie one end of the string into a loop and suspend the book in it.
5. Lay the book on the bottom of the box, directly under the center of the broom.
6. Raise the string straight up.
7. Use the scissors to cut the string about one foot (30 cm) above the broom.
8. Wind the excess string around the broom in a counterclockwise direction, and tape the end of the string to the broom.
9. Use your hand to turn the ruler handle in a clockwise direction.
10. Count the turns it takes to raise the book so that its lower edge is about 2 inches (5 cm) above the bottom of the box.

Results

The broom rotates in the same direction as does the ruler handle. The string winds around the broom handle, causing the book to rise. The number of turns depends on the size of the book.

Why?

A wheel and axle is a simple machine made up of a large wheel attached to a shaft called an axle. The wheel and axle turn together. The broom and ruler form a wheel and axle: the ruler acts as the wheel, while the broom handle acts as the axle. This, and all wheel-and-axle machines, acts like a first-class lever (see Experiment 1). The wheel and axle behaves as if a straight bar runs through it, as indicated by the diagram. The radius of a circle is the distance from the edge of the circle to its center. The radius of the circle formed by the turning ruler is similar to the effort arm of a lever, and the radius of the axle is similar to the lever's load arm. As in a lever, a load is easily moved by a wheel and axle when its effort arm (in this case, the radius of the wheel) is longer than the load arm (the radius of the axle).

Let's Explore

1. The mechanical advantage of a lever increases if the effort arm is longer than the load arm. Would the mechanical advantage of a wheel and axle increase by increasing the effort arm? Repeat the experiment, but increase the effort arm by replacing the ruler with a longer stick such as a yardstick (meterstick).
2. Would increasing the radius of the axle affect the results? Increase the radius of the broom handle by cutting holes in the ends of a cylindrical cardboard container (such as a salt or oats box) and sticking the broom handle through the container. Tape the string to the container, and repeat the original experiment.

Show Time!

1. Use pencils instead of the broom and ruler to construct smaller models of the wheel and axle. Display this reduced-scale model, along with photographs of the original models.
2. Other simple machines, such as the pulley and gears, act like levers. Use the example diagrams to illustrate the similarities of pulleys and gears to a lever.