Oscillation can travel through mediums such as air or water without carrying water along with them. These mechanical disturbances are called waves. Waves are one of the most common natural phenomena.
Sound travels very fast but it is not infinite. Sound is a wave or disturbance that travels at a definite speed.
The "Big Bang" is an example of a wave where a disturbance in one place led to reactions in another.
When any stable mechnical system is disturbed nature's response is simple harmonic motion, where the disturbance in one place is passed on to the next as a mechanical wave.
In a crystaline solid, linkage is weak where disturbances travel slowly, and linkage is strong where disturbances travel rapidly. Any waves that propogate through a medium are mechanical waves. Impulses pass through a crystal from atom to atom because each atom is bound together to an equilibrium position by electrical forces. These atoms act mechanically like masses connected by springs.
Musical instruments send waves through the air with an amplitude the size of the disturbance which is preserved as the waves moves along. The time for each complete cycle is known as a period. The inverse of this is the frequency on which the tone of an instrument depends. The definite distance from one compression to the next is known as the wavelength.
wavelength = T v (speed of wave)
frequency x wavelength = v where speed is always the same.
In the case of water waves, speed decreases as they approach the shore. Long waves travel faster than shorter waves, however all waves obey the same principles.
Harmonic oscillations respond and spring back.
For masses on a spring:
v = a sqrt(k/m)
Gravity and the length of the water wave determine speed.
v = sqrt ( g (wavelength) / 2pi)
Masses on a spring produce waves in the direction of connection known as longitudal waves.
Waves that travel throughout a solid are known as transverse waves, however water waves are classified in neither of these categories.
Each water molecule moves on the surface in little circles where each circle is slightly offset from the next.
v = sqrt (g h) in shallow water
Waves of sound vibrate air into motion, expanding and compressing density with each vibration. This is why sound carries the same frequency as the source driven by the force that produces change in pressure as density increases and decreases. Below is a video that physically displays sound waves:
v = sqrt (pressure/density)
Newton attempted to find the speed at which sound traveled along the corridors at Trinity University and determined that the sound waves traveled at a speed of 979 ft/sec. However, Newton was incorrect and William Derham discovered that the speed of sound was in fact 1142 ft/sec. This discrepency is due to the fact that air heats up as it is compressed and travels back faster. This was not discovered until a century later.
Below is a video that explores the nature of waves in depth:
Sunday, November 27, 2011
Sunday, November 20, 2011
Lesson 17 Resonance
When a force is applied repeatedly at the natural frequency of any system, large amplitude oscillations result, this is the phenomenon of resonance.
A tuning fork is a common tool used to tune the piano. How does this device function? The tuning fork sets air molecules into harmonic motion. Air works as an elastic medium that is a good conductor of traveling oscillations waves. The tuning fork pushes air molecules into waves to the natural frequency of the tuning fork. When the pitch of the piano is equal to the pitch of the tuning fork, the waves from the piano can disturb its Naturally oscillating systems. Below is a video of a tuning fork being used to tune a piano:
A = a(0)/ (omega(0)^2 – (omega)^2)
If the frequency of an object is close to its natural frequency, spectacular things can happen. On of the most famous is the shattering of a wine glass due to the frequency of a persons voice. Here is a video that demonstrates the shattering of a glass:
It is important to note that glass is a viscous fluid. If glass was not viscous, there would be no such thing as a glass window. Forces can be sent out at many frequencies. One of the most detrimental forces are earthquakes. The force of earthquakes resonate at a very low frequency that causes buildings to shake and deteriorate as shown below:
Aoelian harps function at certain wind speeds, which cause vorteces to peel off at the relative frequency of the wire. The "sea organ" below functions similarily:
Most systems containing vorteces are all examples of resonance, an important aspect of physics.
On July 1st, 1940, a delegation of citizens met in Washington states to engineer the Tacoma Narrows Bridge. This bridge was the longest suspension bridge in the world, but was destroyed due to the force of resonance. The word resonance itself is the Latin noun for “echo.” Below is footage of the Tacoma Narrows Bridge:
With music, the pleasant sounds are strictly due to the resonance of the instrument. All instruments resonate equally no matter what note is played. On the violin or cello, the strings vibrate hundreds to thousands of cycles per second and cause the whole instrument to vibrate at the same frequency. Every vibration gives the instrument’s “sound box” a push so that the “sound box” vibrates resonantly. The vibrations excite resonant vibrations of the air inside the sound box.
A tuning fork is a common tool used to tune the piano. How does this device function? The tuning fork sets air molecules into harmonic motion. Air works as an elastic medium that is a good conductor of traveling oscillations waves. The tuning fork pushes air molecules into waves to the natural frequency of the tuning fork. When the pitch of the piano is equal to the pitch of the tuning fork, the waves from the piano can disturb its Naturally oscillating systems. Below is a video of a tuning fork being used to tune a piano:
Resonance obeys the differential equations of a mass on a spring:
F = -k x
m a = -k x
m (d^2x/dt^2) = -k/m x x = c sin (omega(0) t)
dx/dt = (omega(0)) c cos(omega(0) t)
d^2x/dt^2 = (-omega(0)^2) c sin (omega(0) t)
(-omega(0)^2) c sin (omega(0) t) = -k/m (c sin (omega(0) t))
omega(0)^2 = k/m
Due to the repetitive force applied while “pumping” on a swing, this motion is considered to be a form of resonance.
F = -k x
F(0)sin (omega t) where the force applied at a different frequency is proportional to F
F = -k x + F(0)sin (omega (t))
m a = -k x + m a(0) sin (omega(t))
d^2x/dt^2 = -kx/m + m/m a(0) sin (omega (t)) = -(omega(0)^2 x + a(0) sin (omega (t))
x = c sin (omega(0) t) + A sin (omega (t))
d^2x/dt^2 = -(omega(0)^2 c sin (omega(0) (t))) – (omega^2 A sin (omega (t)))
-(omega(0)^2 c sin (omega(0) (t))) – (omega^2 A sin (omega (t))) = -(omega(0)^2 c sin (omega(0) (t))) – (omega^2 A sin (omega (t))) + a(0) sin (omega (t))
A sin (omega (t)) = a(0)/ (omega(0)^2 – (omega)^2) sin (omega (t))
The size of the oscillations depends on the size of the force a(0) and how close its frequency (omega) is to the natural frequency omega(0).
The amplitude of forces oscillations is sensitive to the frequency.A = a(0)/ (omega(0)^2 – (omega)^2)
If the frequency of an object is close to its natural frequency, spectacular things can happen. On of the most famous is the shattering of a wine glass due to the frequency of a persons voice. Here is a video that demonstrates the shattering of a glass:
It is important to note that glass is a viscous fluid. If glass was not viscous, there would be no such thing as a glass window. Forces can be sent out at many frequencies. One of the most detrimental forces are earthquakes. The force of earthquakes resonate at a very low frequency that causes buildings to shake and deteriorate as shown below:
Aoelian harps function at certain wind speeds, which cause vorteces to peel off at the relative frequency of the wire. The "sea organ" below functions similarily:
Most systems containing vorteces are all examples of resonance, an important aspect of physics.
Lesson 16 Harmonic Motion
Newton’s second law F = m a combined with a restoring force leads to a motion that repeats itself over a period of time. This is known as harmonic motion. Galileo studied a lamp in a church and timed the lamp’s swing. Galileo observed that each swing took the same amount of time even as the motion died down. This observation led to the development of the first accurate clock. In other words, pendulums can be used to keep time.
Time must be “kept” in music which is also an example of harmonic motion. Musical instruments share a special property with bobbing weights. Both the weights and instruments create vibrations at a certain frequency which produces a certain pitch that doesn’t change as the motion decreases. There are many factors that determine the tone of a musical instrument including: length of string, size, shape, and the technique with which the instrument is played. In the physics behind music, one factor never varies. Once the tone has been produced the pitch is the same even though the vibrations diminish. The pitch remains constant because of force, the F in the equation F = m a.
In a certain position all forces are balanced, however, when a spring is stretched it attempts to pull the mass back to its original position. The farther the mass moves the greater the force to pull the mass back to its original position. Conversely, when a spring is compressed it tries to push the mass back, which ever direction the mass moves, a force emerges to counter the displacement. The combination of this force and the mass’s inertia will be the key to keeping time.
At each point in its motion, the net force is proportional to the distance x of the mass from its equilibrium position and in the opposite direction.
The equation is F = -k x where the value of k depends on how stiff the spring is.
In earlier periods of history, there was a constant need for objects that keep accurate time. Cycles in nature, lunar eclipses, solar eclipses, and solar cycles were all used to tell time. However, with the discovery of harmonic motion, clocks were developed to keep accurate time because all clocks oscillate with precision following the most inexorable law in physics F = m a
F = m a
F = m d^2x/dt^2
F = -k x
d^2x/dt^2 = -k/m (x)
This equation describes the simple harmonic motion of not only a mass on a spring but any system that when disturbed, returns to equilibrium with a force proportional to the distance.
x = A sin(omega(t))
dx/dt = A omega cos(omega(t))
d^2x/dt^2 = -k/m (x)
(omega)^2 == k/m
(omega) = sqrt (k/m)
Potential energy = du/dx = -F
integral(du/dx) = kx
U = k(½)x^2 while K = (½) m v^2
As a ball rolls in the curved shaped bowl there is a continual interchange between potential and kinetic energy.
U = k(½)x^2 K = (½) m v^2
x = A sin(omega(t)) v = omega A cos(omega(t))
U = k(½) A^2 sin^2(omega(t))
K = (½) m omega^2 A^2 cos^2(omega(t))
E = U + K
It takes the same time for a pendulum to complete a swing even if motion dies down. All pendulums of the same length oscillate at the same rate regardless of their mass. In the case of a falling body, if all bodies fall at the same rate, regardless of their mass, then all pendulums should oscillate at the same rate regardless of mass. All bodies fall to earth with the same constant acceleration. The force of gravity, which depends on the mass of the pendulum, will cancel the mass in the equation F = m a. In general, if an object is disturbed it exhibits simple harmonic motion. Below is a clip from the Mechanical Universe that explains harmonic motion:
Time must be “kept” in music which is also an example of harmonic motion. Musical instruments share a special property with bobbing weights. Both the weights and instruments create vibrations at a certain frequency which produces a certain pitch that doesn’t change as the motion decreases. There are many factors that determine the tone of a musical instrument including: length of string, size, shape, and the technique with which the instrument is played. In the physics behind music, one factor never varies. Once the tone has been produced the pitch is the same even though the vibrations diminish. The pitch remains constant because of force, the F in the equation F = m a.
In a certain position all forces are balanced, however, when a spring is stretched it attempts to pull the mass back to its original position. The farther the mass moves the greater the force to pull the mass back to its original position. Conversely, when a spring is compressed it tries to push the mass back, which ever direction the mass moves, a force emerges to counter the displacement. The combination of this force and the mass’s inertia will be the key to keeping time.
At each point in its motion, the net force is proportional to the distance x of the mass from its equilibrium position and in the opposite direction.
The equation is F = -k x where the value of k depends on how stiff the spring is.
In earlier periods of history, there was a constant need for objects that keep accurate time. Cycles in nature, lunar eclipses, solar eclipses, and solar cycles were all used to tell time. However, with the discovery of harmonic motion, clocks were developed to keep accurate time because all clocks oscillate with precision following the most inexorable law in physics F = m a
F = m a
F = m d^2x/dt^2
F = -k x
d^2x/dt^2 = -k/m (x)
This equation describes the simple harmonic motion of not only a mass on a spring but any system that when disturbed, returns to equilibrium with a force proportional to the distance.
x = A sin(omega(t))
dx/dt = A omega cos(omega(t))
d^2x/dt^2 = -A (omega)^2 sin(omega(t))
d^2x/dt^2 = -w^2 xd^2x/dt^2 = -k/m (x)
(omega)^2 == k/m
(omega) = sqrt (k/m)
Frequency = omega = 2pif where omega (radians per second) is equal to 2pi (radians cycle) multiplied by the frequency (cycles per second).
Principles of uniform circular motion and harmonic motion are closely related as viewed in the video below:
Potential energy of harmonic motion can be modeled by a curved shaped bowl.Potential energy = du/dx = -F
integral(du/dx) = kx
U = k(½)x^2 while K = (½) m v^2
As a ball rolls in the curved shaped bowl there is a continual interchange between potential and kinetic energy.
U = k(½)x^2 K = (½) m v^2
x = A sin(omega(t)) v = omega A cos(omega(t))
U = k(½) A^2 sin^2(omega(t))
K = (½) m omega^2 A^2 cos^2(omega(t))
omega^2 = k/m
m(omega)^2 = kE = U + K
U+K = ½ k A^2
E = ½ k A^2 where the total energy is constant although potential and kinetic energy change.It takes the same time for a pendulum to complete a swing even if motion dies down. All pendulums of the same length oscillate at the same rate regardless of their mass. In the case of a falling body, if all bodies fall at the same rate, regardless of their mass, then all pendulums should oscillate at the same rate regardless of mass. All bodies fall to earth with the same constant acceleration. The force of gravity, which depends on the mass of the pendulum, will cancel the mass in the equation F = m a. In general, if an object is disturbed it exhibits simple harmonic motion. Below is a clip from the Mechanical Universe that explains harmonic motion:
Sunday, November 13, 2011
Lesson 15 Conservation of Momentum
The momentum of an object is m x v; when no external forces act on a system the total momentum is constant, this is known as the conservation of momentum. The total quantity of motion in the universe is fixed. In other words, if a body is not interferred with it will move at a constant speed in a straight line (Inertia). The body does not come to rest but transfers motions to other bodies; the total energy is conserved. The change in motion is proportional to the force impressed, and is made in the same direction of the straight line in which the force is impressed.
Motion = Momentum
p = m v
Momentum = Mass x Velocity
All of Newton's laws can be represented by differential equations:
F = dp/dt (second law)
A single particle of some mass has p = m v
F = d p
dt
No force 0 = d p
dt
p is constant and m v is constant as the motion of the object is constant
Billiards is a game where the conservation of momentum heavily applies. For instance, if a ball is traveling in a straight line (second law, inertia) it has momentum. If two billiard balls come in contact with each other, each ball applies a momentary force causing momentum to change. According to Newton's third law, this change is equal and opposite.
F1 = -F2
dp1/dt = -dp2/dt
d/dt(p1 + p2) = 0 because the total momentum of two balls taken together does not change and is constant.
This rule applies to any number of balls and also to the atoms of which the balls are made. Momentum is always conserved. Each ball is composed of atoms and smaller parts supplying equal and opposite forces to each other. Each ball behaves as if it were a single body with all its mass concentrated at a single point. This is known as the center of mass, where focus must be drawn when calculating velocity and acceleration of a compound body when no net outside force acts on a compund system. No matter what happens to its individual parts the center of mass continues to move at a constant speed in a straight line. Recoil, as when shooting a shotgun, is a prime example of conservation of momentum.
Below is a video that shows how the center of mass moves at a constant rate with the conditions stated above:
The conservation of energy has many forms, as enrgy is conserved strictly and absolutely no matter the masses of the bodies, or type of energy.
The sum of the momentum of all bodies is a conserved quantity that is always the same even with two or more bodies. When there is no outside force, the center of mass moves at a constant velocity. For instance, a planet pulls a moon just as the moon pulls the planet with equal and opposite force.
F1 + F2 = 0, when the derivative of something is zero, the original value was constant.
p = m v
v = p/m
Kinetic energy: k = 1/2 m v ^2
k = 1/2 m (p/m x p/m)
k = p^2/2m
One ball strikes another, this reveals that at rest, there are only two possible outcomes:
1.) p0 = p1 + p2
This is a vector equation that form a triangle. In the collision of billiard balls, only kinetic energy is observed (ignore heat from collison), and kinetic energy is also conserved.
k0 = k1 + k2 k = p^2/2m
p(0)^2/2m = p(1)^2/2m + p(2)^2/2m
p(0)^2 = p(1)^2 + p(2)^2 (The pythagorean theorem)
p(1) is perpendicular to p(2), so when one ball strikes another, the balls come off at right angles.
p(0) = p(1) + p(2) p(0)^2 = p(1)^2 + p(2)^2
2.) p(0) = p(2) p(0)^2 = p(2)^2
The ball transfers its momentum to the other ball and stops.
Physicists use collisions as the sole method for studying the subatomic world.
Descartes chose to look at nature in terms of mathematics and pictured philosophy as a tree. Where the base of the tree is "physics" with all other sciences branching from it.
Below is a video that explains the conservation of momentum in mathematical terms:
Motion = Momentum
p = m v
Momentum = Mass x Velocity
All of Newton's laws can be represented by differential equations:
F = dp/dt (second law)
A single particle of some mass has p = m v
F = d p
dt
No force 0 = d p
dt
p is constant and m v is constant as the motion of the object is constant
Billiards is a game where the conservation of momentum heavily applies. For instance, if a ball is traveling in a straight line (second law, inertia) it has momentum. If two billiard balls come in contact with each other, each ball applies a momentary force causing momentum to change. According to Newton's third law, this change is equal and opposite.
F1 = -F2
dp1/dt = -dp2/dt
d/dt(p1 + p2) = 0 because the total momentum of two balls taken together does not change and is constant.
This rule applies to any number of balls and also to the atoms of which the balls are made. Momentum is always conserved. Each ball is composed of atoms and smaller parts supplying equal and opposite forces to each other. Each ball behaves as if it were a single body with all its mass concentrated at a single point. This is known as the center of mass, where focus must be drawn when calculating velocity and acceleration of a compound body when no net outside force acts on a compund system. No matter what happens to its individual parts the center of mass continues to move at a constant speed in a straight line. Recoil, as when shooting a shotgun, is a prime example of conservation of momentum.
Below is a video that shows how the center of mass moves at a constant rate with the conditions stated above:
The conservation of energy has many forms, as enrgy is conserved strictly and absolutely no matter the masses of the bodies, or type of energy.
The sum of the momentum of all bodies is a conserved quantity that is always the same even with two or more bodies. When there is no outside force, the center of mass moves at a constant velocity. For instance, a planet pulls a moon just as the moon pulls the planet with equal and opposite force.
F1 + F2 = 0, when the derivative of something is zero, the original value was constant.
p = m v
v = p/m
Kinetic energy: k = 1/2 m v ^2
k = 1/2 m (p/m x p/m)
k = p^2/2m
1.) p0 = p1 + p2
This is a vector equation that form a triangle. In the collision of billiard balls, only kinetic energy is observed (ignore heat from collison), and kinetic energy is also conserved.
k0 = k1 + k2 k = p^2/2m
p(0)^2/2m = p(1)^2/2m + p(2)^2/2m
p(0)^2 = p(1)^2 + p(2)^2 (The pythagorean theorem)
p(1) is perpendicular to p(2), so when one ball strikes another, the balls come off at right angles.
p(0) = p(1) + p(2) p(0)^2 = p(1)^2 + p(2)^2
2.) p(0) = p(2) p(0)^2 = p(2)^2
The ball transfers its momentum to the other ball and stops.
Physicists use collisions as the sole method for studying the subatomic world.
Descartes chose to look at nature in terms of mathematics and pictured philosophy as a tree. Where the base of the tree is "physics" with all other sciences branching from it.
Below is a video that explains the conservation of momentum in mathematical terms:
Sunday, November 6, 2011
Lesson 14 Potential Energy
In 1711 Ruđer Bošković, a diplomat, architect, scientist, and writer, proposed the idea that all matter is made up of point masses, and when masses are far apart, force acts between the two masses. Bošković was in fact correct. For example if a force is graphed against position, the zeroes of the graph are points of no force or equilibrium. However, these points of equilibrium are both stable and unstable. A positive force is repulsive while a negative force is attractive. Therefore, a point with a negative force on the left and a positive force on the right is at unstable equilibrium while a point with a positive force on the left and a negitive force on the right is at stable equilibrium. Here is an image of Bošković's work below:
From these findings, it was believed that atoms are bound into stable webs of matter, however, this was not a scientific idea because it could not be readily tested. In the following centuries, John Dalton discovered atoms while Michael Faraday studied fields of force. From these advances it was found that every piece of matter in a solid is in stable equilibrium, unlike the webs of stability predicted by Bošković.
The total amount of energy never decreases because energy is strictly and absolutely conserved. Potential energy depends on position, such as a tank of gasoline, where the positions of the atoms in the molecules of the gasoline determine the potential energy becasue an atoms potential energy depends on its position in the matter it's bound to. Potential energy can be both positive and negative without changing effect where F = -du/dx. The higher above earth an object is, the more gravitational potential energy the object has because potential energy changes with the objects position. Therefore, the closer to the ground an object is, the less potential energy it has.
Gasoline:
Kinetic energy is related to speed, where the faster an object travels the more kinetic energy it has while the slower an object travels the less kinetic energy it has.
Any body can trade potential energy for kinetic energy by trading position for speed.
Here is a video that displays the conservation of energy as potential energy tranfers into kinetic energy:
Molecules in oil have great potential enrgy, as the atoms are bound together by the electrical force between atoms. When the oil atoms are ignited, the molecules rearrange themselves into other forms of matter with less potential energy.
Here is a video that displays the enormous amount of potential energy of oil molecules:
On the other hand, a fire hose has initial potential energy as the wtaer enters the hose, kinetic as the water leaves the hose, and potential energy as gravity influences the path of the water. Work can be described as a change in energy:
Take the lifting of a vessel from one height to another:
Rf
W = integral (Fdr) F = G m Me
RE r^2
Rf
= integral (G m Me dr)
RE r^2
Rf
= GmMe integral (dr/r^2)
RE
Rf
= -GmMe/r |
RE
= -GmMe/Rf - (-GmMe/RE)
u = -GmMe/r
W = uf - uE of the change in potential energy
If the ball is lifted to infinity it has a potential energy of 0, and also on the surface or at ground level.
(-GmMe/RE) + 1/2 (mv^2) = 0 because kinetic energy must balance out potential energy.
Therefore, in the case of a rocket leaving the earth's surface u + k = 0 to escape from the earth and reach infinity where:
V = sqrt ( 2 G Me/Re ) and the rocket will escape is traveling at 11 km/sec
In the case of a firefighter:
Potential Energy = mgh m = 90kg of firefighter
J = 10 m/s^2
The height of the burning building is 30m
= 27000J
420 = 1 calorie of heat
About 6400 calories
However 1 food Calorie is equivalent to 1000 heat calories, therefore it would take to firefighter about 6.4 Calories of food storage.
Work = Force x Height
The human body is actually very inneficient because it uses most of its stored energy to mantain basic bodily functions. In the terms of physics, potential energy is relative to the ground, therefore if one climbs a ladder and returns to the ground, no net work has been accomplished.
Here is a video that describes the distinct difference between kinetic and potential energy:
The total amount of energy never decreases because energy is strictly and absolutely conserved. Potential energy depends on position, such as a tank of gasoline, where the positions of the atoms in the molecules of the gasoline determine the potential energy becasue an atoms potential energy depends on its position in the matter it's bound to. Potential energy can be both positive and negative without changing effect where F = -du/dx. The higher above earth an object is, the more gravitational potential energy the object has because potential energy changes with the objects position. Therefore, the closer to the ground an object is, the less potential energy it has.
Gasoline:
Kinetic energy is related to speed, where the faster an object travels the more kinetic energy it has while the slower an object travels the less kinetic energy it has.
Any body can trade potential energy for kinetic energy by trading position for speed.
Here is a video that displays the conservation of energy as potential energy tranfers into kinetic energy:
Molecules in oil have great potential enrgy, as the atoms are bound together by the electrical force between atoms. When the oil atoms are ignited, the molecules rearrange themselves into other forms of matter with less potential energy.
Here is a video that displays the enormous amount of potential energy of oil molecules:
On the other hand, a fire hose has initial potential energy as the wtaer enters the hose, kinetic as the water leaves the hose, and potential energy as gravity influences the path of the water. Work can be described as a change in energy:
Take the lifting of a vessel from one height to another:
Rf
W = integral (Fdr) F = G m Me
RE r^2
Rf
= integral (G m Me dr)
RE r^2
Rf
= GmMe integral (dr/r^2)
RE
Rf
= -GmMe/r |
RE
= -GmMe/Rf - (-GmMe/RE)
u = -GmMe/r
W = uf - uE of the change in potential energy
If the ball is lifted to infinity it has a potential energy of 0, and also on the surface or at ground level.
(-GmMe/RE) + 1/2 (mv^2) = 0 because kinetic energy must balance out potential energy.
Therefore, in the case of a rocket leaving the earth's surface u + k = 0 to escape from the earth and reach infinity where:
V = sqrt ( 2 G Me/Re ) and the rocket will escape is traveling at 11 km/sec
In the case of a firefighter:
Potential Energy = mgh m = 90kg of firefighter
J = 10 m/s^2
The height of the burning building is 30m
= 27000J
420 = 1 calorie of heat
About 6400 calories
However 1 food Calorie is equivalent to 1000 heat calories, therefore it would take to firefighter about 6.4 Calories of food storage.
Work = Force x Height
The human body is actually very inneficient because it uses most of its stored energy to mantain basic bodily functions. In the terms of physics, potential energy is relative to the ground, therefore if one climbs a ladder and returns to the ground, no net work has been accomplished.
Here is a video that describes the distinct difference between kinetic and potential energy:
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