Climbing to the top of Mount Everest is hard. But, it's slightly easier than you might think as people weigh less as they climb to the top. Let WE be a person's weight on top of Mount Everest and WS be their weight at sea level. What is the value of 1−WE/WS?
Details and assumptions:
+ Assume the earth (other than Everest) is a sphere of mass 6×1024 kg and radius 6,370 km.
+ The top of Mount Everest is 8,848 m above the surface of the earth.
Weight is inversely proportional to the square of the distance from the center of the Earth.
WE/WS = [6370/(6370+8.85)]^2
= 0.9972
1 - (WE/WS) = 2.77*10^-3
0.27% of the person's weight is "lost" at the summit of Everest.
Still a simple careless mistake :
1-9972=0.0028 nt 27.:)
To find the value of 1 - WE/WS, we need to understand the relationship between weight and gravitational force.
The weight of an object is determined by the gravitational force acting on it. The force of gravity depends on the mass of the object and the distance from the center of the Earth. The higher you go, the farther you are from the center of the Earth, and hence, the weaker the gravitational pull. Therefore, your weight decreases as you climb Mount Everest.
To calculate the weight at the top of Mount Everest (WE), we need to consider the weight at sea level (WS) and the change in altitude.
First, we need to find the mass of the object. Mass is constant regardless of location. Let's assume the person's mass is M.
Using the universal law of gravitation, we can calculate the weight at sea level (WS):
WS = (G * M * Me) / Re^2
where G is the gravitational constant (approximately 6.674 × 10^-11 m^3 kg^-1 s^-2), Me is the mass of the Earth (6×10^24 kg), and Re is the radius of the Earth (6,370 km or 6,370,000 m).
Next, we calculate the weight at the top of Mount Everest (WE):
WE = (G * M * Me) / (Re + He)^2
where He is the height of Mount Everest (8,848 m).
Now, we can calculate the value of 1 - WE/WS:
1 - WE/WS = 1 - ((G * M * Me) / (Re + He)^2) / ((G * M * Me) / Re^2)
Simplifying the equation further:
1 - WE/WS = 1 - (Re^2 / (Re + He)^2)
Plugging in the values for Re and He:
1 - WE/WS = 1 - (6,370,000^2 / (6,370,000 + 8,848)^2)
Calculating the expression gives us the value of 1 - WE/WS.