The Burj Khalifa in Dubai is the world's tallest building. It rises to an amazing 828 meters above the ground. If you were to get to the top using the stairs, you would climb a total of 3,234 steps!
If each of these steps has a depth of 20 cm, calculate the total work done by a man weighing 800 N who climbs to the top of the stairs.
Answer (3)
I don't understand what you mean by "depth" of the steps. The flat part of the step has a front-to-back dimension, and the 'riser' has a height. I don't care about the horizontal dimension of the step because it doesn't add anything to the climber's potential energy. And if the riser of each step is 20cm high, then 3,234 of them only take him (3,234 x 0.2) = 646.8 meters up off the ground. So something is definitely fishy about the steps.
Fortunately, we don't need to worry at all about the steps in order to derive a first approximation to the answer ... one that's certainly good enough for high school Physics.
In order to lift his bulk 828 meters from the street to the top of the Burj, the climber has to provide a force of 800 newtons, and maintain it through a distance of 828 meters. The work [s]he does is (force) x (distance) = ***662,400 joules. ***
The question involves calculating the total work done by a man of weight 800N who climbs to the top of the stairs at the Burj Khalifa in Dubai. Since work done can be calculated using the formula Work = Force x Distance, and the force here is the weight of the man which is 800N. To find the total distance climbed, we need to multiply the number of steps with the height of each step (the rise of the stairs). Given that there are 3234 steps and each step has a depth of 20cm, which is equivalent to 0.20 meters.
First, calculate the total height climbed:
Total height climbed = Number of steps x Height of each step
Total height climbed = 3234 steps x 0.20 m/step
Total height climbed = 646.8 m
Next, calculate the total work done:
Work done = Weight x Height climbed
Work done = 800N x 646.8 m
Work done = 517,440 Joules
Trefore, the total work done by the man to climb to the top of the stairs is 517,440 Joules.
The total work done by a man weighing 800 N climbing to the top of the Burj Khalifa at a height of 828 meters is 662,400 joules. This is calculated using the formula for work, multiplying his weight by the height climbed. The calculation assumes ideal conditions without friction or other energy losses.
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