The Burj Khalifa in Dubai is the world\'s tallest building. The structure is 828 m (2,716.5 feet) and has more than 160 stories. A tourist is obviously using the elevator to reach their hotel room and after a long ride finally arrives at the correct floor where the tourist has -181000 J of potential energy. If the 183 lb tourist has zero potential energy at the top of the building, how high is the hotel room from the ground? The acceleration due to gravity is 9.81 m/s2.
-M*g*Y = -181,000 J
where Y is the distance to the top.
M = 83.2 kg
Y = 222 meters
Since the total structure height is 828 m, the distance from the ground is
828 - 222 = 606 m.
To solve this problem, we can use the concept of potential energy and the equation:
Potential Energy = (mass) * (acceleration due to gravity) * (height)
We are given the potential energy of the tourist at the correct floor, which is -181000 J. We are also given that the tourist has zero potential energy at the top of the building. We need to find the height of the hotel room from the ground.
First, let's convert the mass of the tourist from pounds to kilograms. We know that 1 pound is approximately equal to 0.4536 kilograms. So, the mass of the tourist is:
Mass = 183 lb * 0.4536 kg/lb = 83.0076 kg (approximately)
Now, let's use the potential energy equation to find the height:
Potential Energy = (mass) * (acceleration due to gravity) * (height)
-181000 J = 83.0076 kg * 9.81 m/s^2 * (height)
Simplifying the equation, we have:
height = -181000 J / (83.0076 kg * 9.81 m/s^2)
Now, let's calculate the height:
height = -181000 J / (83.0076 kg * 9.81 m/s^2)
height ≈ -181000 J / 813.984 N*m/kg
height ≈ -222.42 meters
The negative sign in front of the height means that the hotel room is below the reference point (top of the building). Therefore, the hotel room is approximately 222.42 meters below the ground.