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?
Several different masses like a set of masses
Unknown mass like a wood block
Slat board 30 cm to 40 cm long
Wedge 5 cm tall
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
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
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.
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
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:
Multiply the distance times the mass for each pair of masses to get the force each mass exerts
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.
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?
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.
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.