you weigh 120 lb at the sidewalk outside the world trade center. Suppose you ride from this level to the top of one of its 1350 ft tower. how much less would you weigh
W₀=mg
g=GM/R².
W=mg´,
g=GM/(R+h)²
ΔW= W₀-W
gravitational constant G =6.67•10⁻¹¹ N•m²/kg²,
Earth’s mass is M = 5.97•10²⁴kg,
Earth’s radius is R = 6.378•10⁶ m.
1 lb
12
To calculate how much less you would weigh at the top of the World Trade Center tower, we need to consider the change in gravitational force as you move vertically away from the Earth's surface.
The acceleration due to gravity is approximately 9.8 meters per second squared (32 feet per second squared). This means that gravity pulls downward on objects at a rate of 9.8 m/s^2.
To calculate your weight at the top of the tower, we can use the formula:
Weight = mass x acceleration due to gravity
First, let's convert your weight from pounds to kilograms. Since 1 pound is approximately equal to 0.4536 kilograms, we can calculate:
Weight = 120 lb x 0.4536 kg/lb = 54.432 kg
Now, let's calculate your weight at the sidewalk level using the formula:
Weight at sidewalk = 54.432 kg x 9.8 m/s^2 = 533.0176 N
Next, let's calculate your weight at the top of the tower. Since the height is given in feet, we need to convert it to meters. Since 1 foot is approximately equal to 0.3048 meters, we can calculate:
Height = 1350 ft x 0.3048 m/ft = 411.48 m
Now, we can calculate your weight at the top of the tower using the formula:
Weight at top = mass x acceleration due to gravity
Weight at top = 54.432 kg x 9.8 m/s^2 = 533.0176 N
Therefore, your weight at the top of the World Trade Center tower would be approximately 533.0176 N.
To calculate how much less you would weigh, we need to subtract your weight at the top from your weight at the sidewalk:
Weight difference = Weight at sidewalk - Weight at top
Weight difference = 533.0176 N - 533.0176 N = 0 N
Therefore, you would not weigh any less at the top of the World Trade Center tower compared to the sidewalk.