# Physics 25 Stable or Unstable

In some states like Montana with lots of high winds, there are signs warning van drivers to stay off the roads when the winds are blowing hard.

Race cars are built low to the ground to go around corners at high rates of speed. Other vehicles going around a corner too fast will tip over.

An object balances at its center of gravity. So, if the center of gravity is over the object’s base, it should be stable and just stand there, right?

Question: Why do objects fall over?

Materials:

Roll of quarters [40 quarters]

Pieces of 1 x 2 of various lengths, at least six pieces [I used 2”, 4”, 6”, 8”, 10” and 12”]

Procedure:

Stack the quarters in a straight stack

The tall straight stack wasn’t quite straight but close. The blue dot shows where the center of gravity is.

Push the stack in the middle until it falls over

When the tall straight stack of quarters fell, only the top half from where the pressure was applied fell. The rest of the stack remained standing.

Stack the quarters so each quarter is slightly [the width of the edge ridge] over from the one below it

The blue dot shows the center of gravity is half way up the stack of quarters and over the edge of the bottom quarter. The stack is stable because it stands but is unstable as a slight push will cause it to fall.

Push the stack from the side it is leaning toward

Restack the quarters as before

Push the stack from the side

Restack the quarters as before

Push from the side it is leaning away from

Pushing on the leaning stack of quarters shifts the center of gravity quickly so it will fall over.

Stack half the quarters in a straight stack

Push over the stack

The blue dot is in the center of the stack of quarters. Pushing the stack is making the center shift.

Restack the quarters and lean the stack

Push this stack over

Stack the wood pieces so the longest piece is on the bottom and each piece is centered

The blue dot showing where the center of gravity is is low and centered over the base.

Push the tower from about half way up the side until it falls over

Stack the wood pieces in the same order but with all the pieces evened up on one side

The blue dot shows where the center of gravity is in the center of the stack. It is low and over the base.

Push the tower from about half way up until it falls over

Stack the wood pieces so the shortest piece is on the bottom centering each piece

Push the stack from about half way up until it falls over

Observations:

Draw each kind of stack and put a dot where the center of gravity is

Describe how the stack of quarters acts as you push it over:

It took a lot of pressure to shove the quarters over off the tall straight stack of quarters.

Straight tall stack:

Leaning tall stack:

Against the lean:

Sideways to the lean:

With the lean:

Straight short stack:

The short leaning stack quickly overbalanced when pushed with the lean. Unlike the straight stack, most of the quarters tipped over not just the top of the stack.

Leaning short stack:

Describe how the wood stack acts as you push it over:

Centered, longest on bottom:

Longest on bottom, flat side

The center of gravity shifted easily when all the blocks were lined up on one edge so the stack tipped over.

Centered, shortest on bottom:

Conclusions:

Where is the center of gravity for each of the stacks, quarters and wood, you built?

Note: Remember how the spoon balanced so your centers of gravity work for the height, width and depth of each stack.

A stable object will stand by itself. Are your stacks of quarters stable?

Pushing against the lean on the leaning stack of quarters first moved the quarters over the base of the stack then over to where they would fall.

An unstable object may stand by itself but is easy to push over. Are any of your stacks of quarters unstable?

What happens to the center of gravity as you push a stack over?

Does the size of the base of the stack of wood affect how stable the stack is? Why do you think this?

How does the center of gravity change as you push over the stacks of wood?

Is it easier to push over a stack with a high center of gravity or a low center of gravity?

Is it easier to push over a stack with the center of gravity square over the base of the stack or when the center of gravity is off center?

How does the center of gravity determine how stable or unstable an object is?

Can an object be both stable and unstable? Why do you think this?

Why is a car more stable going around sharp curves than a van?

What I Found Out:

It was difficult to stack the 40 quarters into a straight stack. Once they were stacked, they didn’t want to fall over. The stack didn’t fall over until I pushed half the stack sideways half way off the stack. This stack was stable. The center of gravity was in the center half way up the stack.

The short stack of quarters was much easier to stack. It was even harder to push over. I had to push the top half more than half way off the stack before it fell over. The center of gravity was in the middle half way up the stack making the stack very stable.

The tall leaning stack of quarters acted differently pushed from the different directions. Pushed from the leaning side the quarters first moved to make a straight stack then fell over the same way as the straight stack. Pushed from the side the quarters acted the same way.

Pushing the stack in the direction in which it was leaning was easy. Almost the entire stack fell over quickly.

The center of gravity was not in the center of the stack. It was moved toward the lean but still half way up. The leaning stack stood up by itself so it was stable to start with but it was unstable too as it would fall over easily.

The center of gravity moved in the direction I pushed the quarters. The stacks fell over when the center of gravity got too far over from the center of the stack.

The regular wood pyramid was very difficult to tip over. The pieces had to be pushed all the way off the ones below before falling. This was a very stable arrangement.

The pyramid stack of wood was very difficult to push over. I had to shove all the pieces off the bottom piece to make them fall.

Even when the edges were in a straight line the boards did not want to fall over until I shoved the boards farther over. It was easier with this stack than with the other stack.

The stack with the big pieces on top was easy to push over. Pushing the top piece an inch made the stack tip over.

The stack of wood with the biggest pieces on the bottom had low centers of gravity. They were very stable. The other stack had a high center of gravity and was unstable.

When pushed, the inverted wood pyramid easily tipped over with the pieces sliding down to the table.

The size of the base did seem important as the pieces had to be pushed off of it before falling. I think I should try different stacking arrangements to see if the base is that important.

Stability seems to depend on the center of gravity as well as the size of the base of an object. Objects with higher centers of gravity are not as stable as those with low centers of gravity. Small bases make it easier to shift the center of gravity and make an object fall over.

Cars have wide bases and low centers of gravity making them very stable. Vans can have wide bases but their centers of gravity are much higher and putting luggage or air conditioning units can make the centers go even higher. Like the two wood pyramids, the van is stable unless going around a corner too fast when the center of gravity shifts making it fall over.

# Physics 24 Center of Gravity

Have you ever picked up a long board? How is it different to pick it up in the middle from picking up one end?
Have you ever watched a waitress balance a tray on one hand?
How do you balance an object on a small point?
Question: How does an object balance?
Materials:
Cardboard from a box
Marker
Scissors
Scale
Spoon
Procedure:

The best way I’ve found for cutting out a rectangle rather than a trapezoid is to measure out across twice, once toward the top and once toward the bottom so the line is straight across the piece of cardboard.

Cut out a square 15 cm on a side, a circle 15 cm diameter, a 15 cm x 20 cm rectangle [These can be a little bigger or smaller.]

The rectangle is cut out by cutting down the line. The entire piece of cardboard was a rectangle and could have been used that way.

Mass the shapes

Massing the rectangle.

Balance each geometric shape on your fingertip marking the place your finger is

The rectangle is longer than its width. This makes finding the balancing point harder as both the length and width must be balanced.

Record where the point is in your Observations

Finding the balancing point for the rectangle took some moving around and a couple of tries to mark it accurately. I marked the first one and tried balancing from that point and found the point was a little further over.

Mark a line straight across each geometric shape going through the marked point
Cut each shape in two on the line
Mass each piece

The mass of the split cardboard rectangle is roughly half the total mass.

Balance the spoon on your finger marking the balancing point
Observations:
Balancing points of the geometric shapes

The mass of the entire cardboard square is 14.32 g.

Masses of the geometric shapes
Masses of the two pieces of each shape:
Balancing point of the spoon
Conclusions:
Is the balancing point always in the measured middle of the object? Why do you think so?
Compare the mass of the object on either side of the balancing point of the cardboard shapes.

The mass of half the cardboard square is 7.16 g , exactly half of the total mass.

Does mass determine the balancing point of an object?
If you could cut the spoon at the balancing point, how do you think the masses of the two pieces would compare?
Another name for this balancing point is the center of gravity. Why is this a good name for the balancing point?

Finding the center of a square without measuring first can take some shifting around but the square finally balances on the tip of my finger.

What I Found Out:
My rectangle was 15 cm x 20 cm. The square was 14 cm x 14 cm. The diameter of the circle was 10 cm.

The mass of the entire cardboard circle is 6.41 g.

The rectangle would sort of balance when my finger was close to the center of the rectangle. It balanced the best, the flattest when my finger was in the center. The same was true for the square and the circle.

Dividing a circle in half even with a center point isn’t easy but still the half is about half the total mass.

The spoon was different. The balancing point was closer to the spoon bowl than to the end of the handle. The balancing point is not always in the middle of a shape.
When I cut the cardboard shapes into two pieces, the two pieces had similar masses. The square halves were the same. The others were tenths of a gram different.

It’s easier to see the circle balances at a point in the center. This is the circle’s center of gravity.

The balancing point seems to be where the mass is the same all around it. If I cut the spoon at the balancing point, I would expect the masses of the two pieces to be very close to the same.
Gravity creates weight. As the balancing point is at the place in an object where the mass and the weight will be the same on all sides, it is at the center of the gravitational pull on the object, the center of gravity.