# Physics 10 Pendulum Motion

Both Galileo and Isaac Newton came up with the laws of motion. Yet we call them Newton’s Laws of Motion. Why?

Time.

Newton could measure time and Galileo could not. Why didn’t Galileo go out and buy a watch? Because there were no watches or clocks in the early 1500’s.

One way Galileo tried to measure time was with his pulse. A pulse is how fast a heart beats. Can you take your pulse?

There are two ways you can take your own pulse. One is in your neck Press your first two fingers against your neck on the side near the top of your trachea or windpipe.

Be sure to use your fingers not your thumb to take your pulse. Your thumb has an artery in it and you will feel this too making your pulse count confused.

The second place is in your wrist. Feel on the inside of your wrist below your hand. There is a hard ridge of bone then a softer area. Several tendons like hard ropes run up your wrist. Press your fingers in beside these below your thumb. You can feel your pulse beat.

Both of these take a little practice. I find it easiest to find the one in my neck. It’s easier to find the wrist pulse in someone else’s wrist.

Galileo would use his pulse to time balls running down a ramp. Stop and think about the last Project. Would Galileo use a steep ramp or one much flatter?

Once you can take your own pulse, watch a clock with a second hand and count the beats for 15 seconds. Get up and run in place or jump up and down 15 times. Now count your pulse again.

Is using your pulse to time some event very accurate?

Galileo decided to try to make a more accurate clock. He used a kind of motion to build a pendulum clock.

For this Project, the pole must be level, the eyes hanging down and far enough from a wall so the nuts will not hit it.

Question: How does a pendulum work?

Materials:

String

Meter long board with small metal eyes or staples in it

A screw eye looks like a screw with a metal loop for a head.

Heavy and light metal nuts, one of each

Stop watch

Ruler

Procedure:

Put two small eyes or staples 20 cm apart near the center of the board

Be sure the eyes or staples have their holes parallel to the board

The two eyes need to be far enough apart for the two pendulums to swing without tangling.

Secure the board between two chairs or tables so the board is level

Cut two lengths of string 60 cm long

Tie a heavy nut to one string and a light one to the other string

Put one string through the eye or staple and tape it to the stick so 15 cm of string hangs from the eye to the nut.

The pendulum string between the knot over the nut and the bottom of the eye is 15 cm. The extra string goes up through the eye, wraps around the pole and is taped in place.

Do the same on another eye with the other string

Pull the nuts up to one side even with the eyes

Released together the heavy and light pendulum nuts swing at the same time to begin with. The string shifted the direction of the swing and changed the timing.

Let the nuts go and watch how they move

Do they move together or is one faster than the other?

Pull one nut to the side level with the eye with the string tight

Pull the nut up level with the eye with the string tight before letting it go.

Start the stopwatch as you drop the nut

Count five times the nut comes back to where it started and stop the stopwatch

Do the same with the other nut

Lengthen the strings to 30 cm and repeat what you just did

Lengthen the strings to 45 cm and repeat these steps

Observations:

Compare how the two nuts swing

Times for five swings:

Five swings of the 15 cm pendulum does not take very long. it is hard to judge when the pendulum reaches the top of a swing.

Light nut, 15 cm:

Heavy nut, 15 cm

Light nut, 30 cm

Heavy nut, 30 cm

Light nut 45 cm

Heavy nut, 45 cm

Analysis:

Calculate the average time for one swing for each trial run

Light nut, 15 cm:

Heavy nut, 15 cm

Light nut, 30 cm

Heavy nut, 30 cm

Light nut 45 cm

Heavy nut, 45 cm

Conclusions:

How accurate do you think your times were? Why do you think so?

Is mass or string length what determines the time of a swing?

The two 30 cm long pendulums are set up.

Can you tie a string so the nut takes five seconds to complete one swing?

Do you think a pendulum will swing forever without being restarted? Why do you think so?

How could Galileo use this type of motion to make a clock?

What do you think would happen if you shook the board while one of the nuts was swinging? Try it and find out.

Would a pendulum clock always be accurate? Why do you think so?

What I Found Out:

I found it difficult to make the strings exactly the same length for the two different nuts. Another problem was when I released the nuts to swing like pendulums. For the first five or six swings they went back and forth then started shifting until they were swinging up and down the pole until they were swinging the opposite way across the pole. This was better when I tied the string off with a loose knot at the eye. It might improve how the nut swung if the string had been tied off each time instead of going through the eye.

The next difficulty was holding the nut up to exactly the same height each time. Putting another board or something else stiff across to bring the nut up to each time would make sure the height was the same each time.

Starting the stopwatch at the same time I released the nut was not as hard but I was probably not as accurate as it seemed I was.

The end result was that my times were probably not as accurate as I wanted them to be. In fact, it is surprising how similar each set of times were.

When I released the heavy and light nuts together, they swung at about the same time. This was the case until the strings shifted. That made me think the mass at the end of the pendulum was not the deciding factor in how fast the pendulum moved.

For my light nut the 15 cm string had an average time of 4.63 sec, the 30 cm string was 6.17 sec and the 45 cm string was 7.65 sec. For the heavy nut the 15 cm string had an average time of 4.75 sec, the 30 cm string was 6.44 sec and the 45 cm string was 7.81 sec.

The longest pendulums take the longest to make five swings. The time of a swing depends on the length not the mass.

Comparing the 15 cm strings gave me 4.63 sec and 4.75 sec. The 30 cm string gave me 6.17 sec and 6.44 sec. The 45 cm string gave me 7.65 sec and 7.81 sec.

This confirmed that the mass of the nuts did not determine the time of a swing. Instead, the longer the string was, the more time a swing took.

Since 5 sec is about half way between the times for the 15 cm and 30 cm strings, I would try a string 22 cm long for a 5 sec swing. I did not have time to test this idea.

I did notice that each swing was a little smaller than the previous swing. Part of this would be the shift in how the string was swinging. Part of this would be friction between the string and eye. Even tying the string to the eye did not stop the pendulum from slowing down. That means a pendulum would not continue swinging forever.

Since a pendulum can swing in the same time if friction is minimized or countered, Galileo could make a pendulum clock. Each swing of the pendulum would have to move a second hand which would move a minute hand which would move an hour hand.

In fact, Galileo did make such a clock. Clocks are still made with pendulums. They use weights to counter the friction and keep the pendulums swinging at the same speed. The pendulums turn gears that move the clock hands to show the time.

Shaking the pole would change how the nuts were swinging. Moving the chair made the swings change size and direction.

A pendulum clock would have to sit still to work properly. If the ground moved or it was on a ship, the pendulum swings would not stay the same so the clock would not be accurate.