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The Physics of Skyscrapers

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by Greg Ross on 21 May 2013

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Transcript of The Physics of Skyscrapers

The Physics of Skyscrapers Newton's 3rd Law What is the force of gravity on a 70kg person staying on the 163rd floor of the Burj Dubai (about 830 meters)? What about the force on the same person if he or she is on the 1st floor (about 1 meter)?


The Burj Dubai weighs 498,961,607 kg, and the distance from earth's surface to its center is 6,371,000 m.

Fg=G(m1m2)/d^2
G=6.67 x 10^-11 Diagram Fa = -Fb
Force of Wind = -Force of Tuned Mass Damper


A 100mph gust of wind exerts a force of 3,000 newtons on the top of a 1,500ft building. What force does the tuned mass damper exert back? Fa=-Fb
3,000N=-3,000N
-3,000N Newton's 3rd Law Newton's 3rd Law Fa=-Fb
6,000N=-6,000N
-6,000N Fa=Fb
9,000N=-9,000N
-9,000N How does a Skyscraper Resist Wind? Taipei 101 How does gravity feel on the top floor of the world's tallest building? 6,371,830 m from Earth's center 6,371,001 m from Earth's center Distance vs. Gravitational Force Distance vs. Gravitational Force Home Insurance Building, Chicago
1885 Preview 1. Wind Resistance
2. Gravitational Effects
3. Force of Earthquakes
4. Energy of a Dropped Object 163rd floor:
Fg=G(m1m2)/d^2
Fg=6.67x10^-11(70kgx(6x10^24kg))/(6,371,830^2)
Fg=689.996N 1st floor:Fg=G(m1m2)/d^2
Fg=6.67x10^-11(70kgx(6x10^24kg))/(6,371,001^2)
Fg=690.176 N What if a 5 mile (8047 meter) high skyscraper was built? What would be the force of gravity on a 70 kg person on the top floor opposed to the first floor (1 meter from surface)? Distance vs. Gravitational Force Top Floor:
Fg=G(m1m2)/d^2
Fg=6.67x10^-11(70kgx(6x10^24kg))/(6,378,047^2)
Fg=688.652N First Floor:
Fg=G(m1m2)/d^2
Fg=6.67x10^-11(70kgx(6x10^24kg))/(6,371,001^2)
Fg=690.176 N Distance vs. Gravitational Force San Francisco Earthquake, 1906 How could San Francisco withstand an earthquake today? Acceleration
0.5 m/s^2 136,077,711kg How much force would be exerted on SF's Transamerica Building in an earthquake? The building is roughly 136,077,711 kg, and during a severe earthquake, the ground can accelerate at roughly 0.5 m/s^2. Newton's 2nd Law F=ma
F=(136,077,711kg)(0.5 m/s^2)
F=68,038,855.5 N Newton's 2nd Law What if an earthquake of the same strength stuck Chicago and the 201,849,000 kg Sears Tower? How much force would be exerted on the Sears Tower? F=ma
F=(201,849,000kg)(0.5m/s^2)
F=100,924,500 N

This is more than 30,000,000 more Newtons of force than the San Francisco tower experienced. Thankfully we aren’t as likely to have earthquakes in Chicago. Newton's 2nd Law "If you dropped a penny from the Empire State Building, it would kill a person on impact." Is there enough
kinetic energy? If you were to drop a 2.5g penny from the top of the 442 meter Sears Tower, what would be its potential energy before you dropped it? What would be its kinetic energy 2 meters from the ground? Assume its terminal velocity is 45 m/s. Potential and Kinetic Energy PE=m x a x h

KE=1/2mv^2 Potential and Kinetic Energy PE=m x a x h
PE=.0025kg x 9.8m/s^2 x 442m
PE=10.83 J KE=1/2mv^2
KE=(1/2)(.0025kg)(45m/s)^2
KE=2.53 J Potential and Kinetic Energy What if you dropped the penny from the top of a future mile high (1609 m) skyscraper? What is its potential energy at the top? Potential and Kinetic Energy PE=m x a x h
PE=(.0025 kg)(9.8m/s^2)(1609m)
PE=39.42 J Review 1. Wind Resistance
2. Gravitational Effects
3. Force of Earthquakes
4. Energy of a Dropped Object Newton's 3rd Law For every action, there is an equal and opposite reaction.

Force of A = -Force of B

Direct Relationship Distance vs. Gravitational Force As you get further from Earth's surface, the gravity you experience decreases.

Inverse Relationship

Fg = 1/d^2 Because distance is inversely related to gravity,
could a skyscraper that is built tall enough cause
a noticeable difference in the force of gravity?



Could it be tall enough to cause a person on the
top floor to age faster than a person on the bottom
floor? Newton's 2nd Law The bigger the mass, the bigger the force. The larger
the acceleration, the larger the force.


F = ma

Direct Relationship Earthquake Force Video Newton's 2nd Law Direct Relationship Direct Relationship Potential and Kinetic Energy Potential Energy results from the position of an object.
Kinetic Energy results from the motion of an object. PE=m x a x h Greater the height, greater the PE.


KE=1/2mv^2 Greater the velocity, greater the KE. Potential and Kinetic Energy
Video Potential and Kinetic Energy Direct Relationship Force of Wind = - Force of TMD Distance vs. Gravitational Force Hong Kong: 6,439 Skyscrapers Tuned Mass Damper
Animation Newton's Laws of Motion 1: Object at rest stays at rest; object in motion stays in motion




2: Acceleration is directly related to net force but indirectly related to mass (or, F=ma) 3: For every action, there is an equal and opposite reaction Inverse Relationship 1: Object at rest stays at rest; object in motion stays in motion Newton's Laws of Motion 2: Acceleration is directly related to Force but indirectly related to mass (or, F=ma) 3: For every action there is an equal and opposite reaction World's Tallest Skyscrapers Fg=G(m1m2)/d^2 G=6.67 x 10^-11
[gravitational constant] m1 & m2 = mass of two bodies (kg)
[mass is the measure of an object's matter] d = distance between the two bodies (m)
[distance is displacement] Gravitational force on first floor is 0.18 N greater than on the top floor.

0.18 N is roughly equal to 1/5 of an apple's weight.

The person on the first floor will age slower than the person at the top, but only by a minuscule amount. The distance between the first floor and the
top floor is about 1.5 Newtons. This difference is the equivalent to
about 1.5 apples. This force is about 5 times the force that the earth’s gravity exerts on the average human. Force of TMD = -3,000 N What if the wind’s force doubles, to 6,000 N? Triples to 9,000 N? F= ma F = force (N)

m = mass (kg)
[mass is the measure of an object's amount of matter]

a = acceleration (m/s^2)
[acceleration is the rate at which an object changes its velocity] Fg = force of gravity exerted on each body (N)
This is the same force as a 1 ton car hitting you
straight on at 168 miles per hour. (75,000 m/s).


This shows the importance of engineering a
building to withstand even the smallest vibrations. F = 68,038,855.5 N Fg = 688.652 N vs Fg = 690.176N Fg = 689.996 N vs Fg = 690.176 N PE = m x a x h PE = potential energy (J)

m = mass (kg)
[mass is the measure of an object's amount of matter]

a = acceleration (m/s^2)
[acceleration is the rate at which an object changes
its velocity]

h = height (m)
[height is the distance from the place of zero PE] KE = 1/2mv^2 KE = kinetic energy (J) m = mass (kg)
[mass is the measure of an object's amount of matter] v = velocity (m/s)
[velocity is the amount of distance covered per unit of time] PE near top = 2.5 calories
KE near bottom = 0.5 calories

Terminal velocity is the reason for this difference. PE = 10.83 J
KE = 2.53 J PE near top = 10 calories PE = 39.42 J All PE All KE Potential
to
Kinetic Taipei 101 Fa = -Fb Force = mass (kg) x acceleration (m/s^2) [mass is the measure of an object's matter]
[acceleration is change of velocity per unit of time] Diagram Diagram Video of Tuned Mass Damper Transamerica Pyramid Diagram What does the future hold? My kind of town... Demo Force on small building
vs. Force on tall building
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