In 1956, Frank Lloyd Wright proposed the construction of a mile-high building in Chicago. Suppose the building had been constructed. Ignoring Earth's rotation, find the change in your weight if you were to ride an elevator from the street level, where you weigh 532 N, to the top of the building.
Welcome back, DrWLS!
At the ground level
weigh = 532 N
W = m*g
at ground g = 9.81 m/sec^2
mass = 532/9.81 = 54.2303 kg
Now at top of the building gravitational accleration will be
g = GM/r^2
so gravitational acceleration is inversely proportional to r^2
g'/g = r^2/r'^2
r = Re = 6.371*10^6 m
1 mile = 1609.34 m
g' = g*(Re/(Re + h))^2
g' = 9.81*(6.371*10^6/(1609.34 + 6.371*10^6))
g' = 9.8075 m/sec^2
your weight will be
W' = m*g'
W' = 54.2303*9.8075
W' = 531.8636 N
Change in weight = 532 - 531.8636
Change in weight = 0.1364 N
CAN ANY ONE HELP WHERE DID I GO WRONG??? BECAUSE IT SAYS THE ANS IS INCORRECT
W = k/r^2
dW/dr = -2kr/r^4
dW = - 2 k dr /r^3
====================
532 N = k / 3959^2
so
k = 532 (3959)^2
so
dW=-2 * [532 * 3959^2]* 1/3959^3
dW = -.2687
I believe that is indeed Dr WLS ! To be sure, how did we get to Nova Scotia and back ?
To find the change in weight when riding an elevator from the street level to the top of the mile-high building, we need to consider the change in distance from the center of the Earth.
The weight of an object is given by the formula:
W = mg
Where W is the weight, m is the mass of the object, and g is the acceleration due to gravity. The acceleration due to gravity varies depending on the distance from the center of the Earth. It can be approximated as:
g' = g * (R / (R+h))^2
where g' is the new acceleration due to gravity, g is the standard acceleration due to gravity on the surface of the Earth (approximately 9.8 m/s^2), R is the radius of the Earth (approximately 6,371 km), and h is the height from the Earth's surface.
In this case, we are looking for the change in weight when going from street level to the top of the mile-high building. The height h can be calculated as:
h = 1 mile * 5280 ft/mi * 0.3048 m/ft
Plugging the values into the equation, we can find the new weight:
W' = m * g'
To calculate the change in weight, we subtract the initial weight (532 N) from the new weight (W'):
Change in weight = W' - W
Substituting the values and calculating will give us the final result.