Thursday, May 23, 2013

# Beach Ball Physics

July 20, 2010 by Jack
Filed under Graph That

Remember when you were a kid and had a beach ball and tried to sit on it
while floating in a lake? Did it ever surprise you how hard it was to get the beach
ball totally under water? I know it did me. We’re going to talk about that today.
Buoyancy is the property that allows us to happily float on an inner tube.
Before we talk about that though we need to talk about water pressure.
Almost all you need to know about water pressure in a lake you can learn
from Dr. Seuss’s classic poem Yertle the Turtle. In this poem, King Yertle, a turtle,
the king of the pond, the ruler of all he could see, decided he didn’t see enough.
In his mind, if he could get up higher, he’d be an even greater ruler. And so he
enlisted the help of the other turtles in the pond. According to the poem, “He
made each turtle stand on another one’s back.” And then he climbed up until he
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was on top of them all. According to the poem:
“And all through the morning, he sat there up high
Saying over and over, “A great king am I!”
Until ‘long about noon. Then he heard a faint sigh.
“What’s that?” snapped the king
And he looked down the stack.
And he saw, at the bottom, a turtle named Mack.
Just a part of the throne. And this plain little turtle
Looked up and said, “Beg your pardon, King Yertle.
I’ve pains in my back and my shoulders and knees
(from Six by Seuss, Random House, 1991)
Mack, the turtle at the bottom of the stack, had to support the weight of all
the turtles above him. And that, basically, is the idea behind both atmospheric
pressure and water pressure. We say that standard atmospheric pressure is 14.7
pounds per square foot. That means that if you were to mark out a one foot by
one foot square on your lawn it would, just like Mack the turtle, have to support
all the air above it, which apparently weighs about 15 pounds.
The same is true of water, except of course water is much heavier than air,
so the pressure adds up faster. For example, if you are 5 feet below the surface of
the water, the water pressure on you is about 2 pounds per square inch. But if
you’re 5000 feet below the surface, where the Gulf Oil deep sea drilling rig is,
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the water pressure is over 2000 pounds per square inch.
There’s one other thing we need to say about water pressure in a lake.
Pick a value for the depth underwater. Let’s say 5 feet. At that depth, the pressure
is the same in all directions. Furthermore, the pressure on a submerged object is
always perpendicular to the surface at each point on the surface. Materials that
have this property are called hydrostatic. If a prospective mom carrying a baby in
her tummy is involved in a car accident, the amniotic fluid surrounding the baby
will cushion the blow. Thanks to hydrostatic pressure.
Finally we can talk about buoyancy. Imagine a can of beans completely
submerged in a lake. (Don’t ask how it got there.)
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What this shows is that the reason for buoyancy is because the bottom of
the can experiences a greater force upward from water pressure than the top part
of the can experiences.
If you do a little math, you can show that the buoyant force on an object in
water is equal to the weight of the water displaced by the object.
So what determines if some object in a lake floats or sinks? Basically we
have two forces competing with each other: the buoyant force and the Earth’s
greater pressure here
because the bottom of
the can is in deeper
water
less water pressure here
because the top of the can
is in shallower water
surface of lake
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gravitational force, which we call the object’s weight. If the weight force is
greater, the object will sink to the bottom. If the buoyant force when the object is
completely submerged is equal to the weight force, object will just barely float.
submerged. If the buoyant force of the completely submerged object is greater
than the object’s weight, then part of the object will be above water.
Why is more of your body out of the water when you float in the Great Salt
Lake in Utah? Because salt water weighs more than regular water. Remember
that the buoyant force upward is equal to the weight of the water you displace.
Heavier water means more buoyant force so you don’t have to displace as much
water. Or, in other words, you float better.
Let’s go back to a boy or girl trying to sit on top of a beach ball in a lake. If
you have a 16 inch diameter beach ball, a boy or girl weighing 75 pounds should
be able to sit on a completely submerged beach ball. But of course it gets real
tricky to actually do it. I always ended up tipping over.
From all this you can probably guess how many friends I had as a child
and, even now, how much fun I am to be with at a family outing at a lake. “Look,
everyone, I’m sitting on top of a beach ball!”
It’s sad in a way, right? But look on the bright side. Who needs friends if
you have a beach ball?