In the episode of Spongebob Squarepants
called Pizza Delivery, one of the best physics related
scenes happens; and this scene is when Spongebob climbs on
top of a rock and rides it. This is improbable, and likely
very impossible, but we're here to find out the physics
behind it.
To begin, we assumed a few things; for this problem Spongebob will be 5 centimeters tall, or .05 meters, and looking at pictures we're going to say the rock is about five times his height. This would mean the height of the rock is .25 meters. Continuing, the rock is assumed to be a box which allows us to find the volume. The density of rock salt is found to be 2.5 grams per centimeter cubed, and the volume of a rock with a 10 cm square base and a height of 25 centimeters is 2500 centimeters cubed. So, we end up finding that this rock Spongebob rides is about 6.25 kilograms.
The next step in our math is to assume a speed, for this project we're going to say that the rock is moving at about sixty miles per hour, given that the above picture makes it look really fast. This speed would end up being 26.82 meters per second. Below is all of the information needed that was found:
Speed of Rock - 26.82 m/s
Mass of Rock - 6.25 kg
says that
momentum is conserved, but for this case, a rock is
starting from rest and just..moving. The momentum would
then be:
p = m v = 6.25 * 26.82 = 167.625 N m
To begin, we assumed a few things; for this problem Spongebob will be 5 centimeters tall, or .05 meters, and looking at pictures we're going to say the rock is about five times his height. This would mean the height of the rock is .25 meters. Continuing, the rock is assumed to be a box which allows us to find the volume. The density of rock salt is found to be 2.5 grams per centimeter cubed, and the volume of a rock with a 10 cm square base and a height of 25 centimeters is 2500 centimeters cubed. So, we end up finding that this rock Spongebob rides is about 6.25 kilograms.
The next step in our math is to assume a speed, for this project we're going to say that the rock is moving at about sixty miles per hour, given that the above picture makes it look really fast. This speed would end up being 26.82 meters per second. Below is all of the information needed that was found:
Speed of Rock - 26.82 m/s
Mass of Rock - 6.25 kg
Now, the momentum equation:
But
something should have, theoretically, transferred its
momentum to the rock for this to happen. So, for this
problem we're going to say there was an invisible mermaid
swimming and she magically transferred her momentum to the
rock or something. Highly unlikely if you ask me, so maybe there was
an elastic collision and this mermaid was just swimming
along and struck this rock. Which would mean we could find
the speed she would have to be going using this equation:
Where vf is the final velocity of the rock, m1 is the mermaid, which we're going to say is 50 kg, m2 is the rock, and vi is the velocity the mermaid was moving with. Using this, we came up with:
Vi = 15.5 m/s
A little more likely, but of course these calculations were done without taking into account the water resistance the creatures felt, and the belief that mermaids exist. It also needs to be clear that it's not just a boulder, it's a rock. As Spongebob said, "The pioneers used to ride these babies for miles."
vf(m1+m2)/2m1=vi
Where vf is the final velocity of the rock, m1 is the mermaid, which we're going to say is 50 kg, m2 is the rock, and vi is the velocity the mermaid was moving with. Using this, we came up with:
Vi = 15.5 m/s
A little more likely, but of course these calculations were done without taking into account the water resistance the creatures felt, and the belief that mermaids exist. It also needs to be clear that it's not just a boulder, it's a rock. As Spongebob said, "The pioneers used to ride these babies for miles."
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