# Stability and Center of Gravity Using Pulleys

This activity uses a pulley and some string to explore the concept of stability and how it is related to an object’s center of gravity. The activity takes 40-45 minutes. Intended for ages 11 and up.

What you’ll need:

1. Push/pull Balance 250 g (PH0035A)
2. Plastic Pulley, Single, 50 mm Diameter (PH0280A)
3. Nylon Suspension Cord approx. 30m (PH0302A)
4. Stapler, paperclips and/or binder clips, tape (duct tape works really well), scissors
5. An old cereal box
6. Paper and pencil to record your observations

Activity Guide:

1. Calibrate the push/pull balance. Hold the balance by the long c-shaped handle and look at the scale on the side. Rotate the white screw so that bottom of the angled section lines up with the top-line of the scale. In the images below, the first is too high, the second is too low, and the third is just right.

2.  Use the push/pull balance to measure the mass of the pulley. The mass is given by the numbers on the right side of the scale. Record the mass in the table below.

3.  Cut the two largest sides off of a discarded cereal box. Be sure to retain the rectangular shape.

4.  Holding the cardboard with the long side on top, cut out a rectangle 0.5 in wide x 2.25 in tall in the center. Do this for both pieces of cardboard in the same place. You can cut one and then use it as a template for the other. This is where we will mount the pulley for our experiment.

Now we are going to do some art. We are going to try to create a tightrope unicyclist. A unicycle is a bicycle with only one wheel – it takes tremendous skill and balance to ride one of these. The pulley wheel will be the unicycle wheel, so you can imagine how big the unicyclist should be relative to the pulley. It’s important that in this experiment the unicyclist will be carrying a balance pole that will curve and bend down toward the corners of the cardboard. Here’s a picture to inspire you. Draw your unicyclist on the blank side of one of the pieces. You can also draw it on the other piece.

5.  Carefully remove the hooks from the pulley. You may need to ask an adult to help you, but it can be done without pliers by bending the hook against the pulley mount.

6.  Use duct tape to tape the pulley to one of the pieces of cardboard. Make sure the cardboard doesn’t rub against the pulley wheel. Attach the other piece of cardboard to the other side using the stapler.

7.  Measure the mass of the unicyclist with the pulley.

Now we need to create the tightrope on which the unicyclist will ride. Tie the string between two firmly fixed points, like between two doorknobs or from a doorknob to a table leg. It is helpful to use a doorknob so you can loosen the tightrope by opening the door. You may need to get creative or ask an adult to help you. It’s much more fun if one attachment point is a bit higher than the other so the unicyclist rides down the tightrope on her own. Before you tie off your tightrope, be sure you thread the string through the bottom opening of the pulley.

You will want the tightrope to be pretty tight like a guitar string. The tightrope should not sag too much with the weight of the unicyclist.

By now you will probably have noticed that the unicyclist won’t stay upright. The unicyclist isn’t stable. A stable object returns to its original position if pushed or bumped slightly. Imagine a simple pendulum – if you pull the pendulum to the side the pendulum swings back toward its original position. The pendulum is stable.

So we need to find a way to make the unicyclist stable. This can be done by ensuring the center of gravity is below the wheel of the unicycle. The center of gravity is the ‘dangling point’. If an object is suspended by any point, the center of gravity will always dangle below the suspension point. Always – no matter where the suspension point is located. This means that every object has one and only one center of gravity.

We can change the center of gravity by adjusting the weight distribution. To move the center of gravity down   we can remove some of the cardboard from the top and add weights to the bottom.

You will want the tightrope to be pretty tight like a guitar string. The tightrope should not sag too much with the weight of the unicyclist.

By now you will probably have noticed that the unicyclist won’t stay upright. The unicyclist isn’t stable. A stable object returns to its original position if pushed or bumped slightly. Imagine a simple pendulum – if you pull the pendulum to the side the pendulum swings back toward its original position. The pendulum is stable.

So we need to find a way to make the unicyclist stable. This can be done by ensuring the center of gravity is below the wheel of the unicycle. The center of gravity is the ‘dangling point’. If an object is suspended by any point, the center of gravity will always dangle below the suspension point. Always – no matter where the suspension point is located. This means that every object has one and only one center of gravity.

We can change the center of gravity by adjusting the weight distribution. To move the center of gravity down we can remove some of the cardboard from the top and add weights to the bottom.

8.  Cut away the upper corners of the cardboard and add paperclips or binder clips to the bottom corners. See the image below. Continue until the unicyclist is stable. Measure the weight and record in the table below.

9.  Optimize the unicyclist by incrementally removing additional cardboard below the balance pole and adjusting the position and number of the paperclips until the silhouette looks as good as you can make it. Remove material slowly because it can’t be put back easily. How light can you make the unicyclist and still have it be stable? Measure the weight and record in the chart below.

Challenge questions:

Do you think the pulley would be stable on its own? If you started over, and you didn’t try to make a unicyclist, where would you add the weight to make the pulley stable? What is the minimum amount of weight required to make the pulley stable? Can you determine this experimentally?

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