# Physics 23 Balancing Force and Mass

Find yourself a half gallon juice or milk plastic jug and fill it two thirds with water. You can use a gallon jug but only half fill it. Set it on a table or stool so it is about waist high.

First stand next to the jug. Grab it and lift it up a foot or so.

Next stand at arm’s length away. Grab the jug and lift it up a foot or so.

What happened to the jug? Did anything change about the jug? What did change?

Question: How can you balance force and mass?

Materials:

Several different masses like a set of masses

Unknown mass like a wood block

Scale

Slat board 30 cm to 40 cm long

Wedge 5 cm tall

Metric ruler

Procedure:

Mass all your different masses unless they are a marked set

Set the wedge on a table top pointing up

Balance the slat on the wedge

I used a piece of scrap wood for a slat so it was not smooth. that made it harder to balance on the wedge. Having more of a flat area on the tip of the wedge would make balancing the slat easier too.

Note: This is easier if the wedge tip is a little flattened. Work slowly moving the slat back and forth a speck at a time finally until the slat seems to balance. It will probably never balance levelly on the wedge. Get as close to the balance point as you can.

Mark the place on the slat where it balances, the mass center point

Set a lighter mass on one end of the slat

Placing a mass on one end of the slat or lever makes that end sink to the table.

Take a heavier mass and move it around on the other length of the slat until it balances

Note: Again the slat will probably not balance levelly on the wedge. Move the heavier mass until you find the point closest to balancing.

A 50 g mass must be closer to the wedge or fulcrum to balance with a 20 g mass on the other end.

Measure the distances from the center point of the slat to each mass

Do this again with another set of masses

Mark the slat halfway from the balancing point to one end of the slat

Place the slat on the wedge so the new place is on the tip of the wedge

Place a heavy mass on the short end of the slat

Take a lighter mass and move it up and down the other end of the slat until the two masses balance

Measure the distances from the mark on the slat to each of the masses

Do this again using other masses

Place the unknown mass block on one end of the slat

Use a mass to balance the slat

Measure the distances

Mass the unknown block

The wood block had a mass of 55.29 g on the scale.

Observations:

Masses of the masses:

Distances to the masses (mark down which mass is where each time):

Distances for the unknown mass:

Mass used to balance the unknown block:

Mass of unknown block:

Analysis:

Multiply the distance times the mass for each pair of masses to get the force each mass exerts

Getting the two masses to balance takes careful nudging of one mass until the slat or lever slowly shifts from one side to the other.

You are using the formula Md = Md where M is mass and d is distance. Use this formula to find the mass of the unknown block.

Conclusions:

Compare the forces exerted for each pair of masses.

Compare your calculated mass for the unknown block to its actual mass.

How could you get the calculated mass and actual mass to be the same?

Why did the effort needed to lift the jug of water change?

If you are playing on a teeter totter with a small child who weighs much less than you do, where would you sit so the child could move up and down instead of being stuck in the air?

A 10 g mass must be twice as far from the wedge as the 20 g mass to balance.

The slat could be considered to be a lever. The wedge is the fulcrum. If you wanted to move a very heavy rock with a lever, where would you place the fulcrum to use the least effort? Why?

What I Found Out

My slat was not smooth. Its thickness varied so the balancing point was not quite in the middle of the slat. My wedge did not have a flattened tip so the slat never really stayed level. I moved the slat then the masses until the slat tipped slowly from one end up to the other end up.

I tried to time my pictures for when the slat was slowly shifting. That is how I got the slat to look so balanced in some of them. I had to get the masses very close to balancing so the slat moved slowly for the picture.

When I used the 50 g and 20 g masses, the distance for the 20 g mass was 21.3 cm and the 50 g distance was 7.7 cm. The forces were 426 g-cm and 385 g-cm.

When I used the 10 g and 20 g masses, the distance for the 10 g was 21.1 cm and the 20 g distance was 11.5 cm. This gave forces of 211 g-cm and 230 g-cm.

Balancing the 10 g and 5 g masses, I had distances of 9.3 cm and 19.8 cm. this gave forces of 93 g-cm and 99 g-cm.

Because my slat was so short, I had to use the 50 g mass to balance the wood block. Could I use a smaller mass if I moved the wedge or fulcrum closer to the block end of the slat? Probably.

I used the 50 g mass to balance the wood block. The mass had a distance of 21.4 cm. The block had a distance of 17 cm. This gave me a calculated mass of 63 g. The mass on the scale was 55.29 g.

It took a lot of time to keep moving the mass a speck at a time to get the balance really close. I got impatient and tried to hurry so I wasn’t as accurate as I should have been.

Having a better wedge with a flat spot so the slat would balance better would help too.

I forgot my metric ruler and used the meter stick. This was long and clumsy making it hard to read the distances accurately.

The jug of water did not change. What did change was the distance from the jug to my shoulder. The force exerted downward by the jug was the distance from me to the jug times the mass of the jug. Increasing the distance increased the force and made the jug seem heavier even though it wasn’t.

Playing on a teeter totter is only fun if both people can go up and down. The heavier person can slide forward so the beam balances better.

A lighter force farther from the wedge or fulcrum can exert more force on the other mass. So I would want the fulcrum close to the rock. that way I can push down a little to push hard on the rock.