Statement:
Zaneta and her friend Late are visiting Paris and decide to climb the Eiffel Tower. Zaneta has a mass of 60 Kg and Kate has a mass of 50 Kg. Zaneta does 180000 J of work in climbing the 1600 steps to the top of the tower. Kate climbed 400 steps.
To find out:
a. The height of the Eiffel Tower
b. The work done by Kate
Solution:
a. Mass of Zaneta (m) = 60 Kg
Acceleration due to gravity (g) = 10 m/s²
Work done (W) = 180000 J
Let the height of the Eiffel Tower be h.
We know the formula of work, i.e., W = mgh
So, putting the given values in the above formula, we get
180000 J = 60 Kg × 10 m/s² × h
or, 180000 J = 600 Kg m/s² × h
or, h = (180000 ÷ 600) m
or, h = 300 m
So, the height of the Eiffel Tower is 300 m.
b. Mass of Kate (m) = 50 Kg
Height of each step of Eiffel Tower = (300 ÷ 1600) m = 0.1875
Height that Kate climbed up in 400 steps = (0.1875 × 400) m = 75 m
Acceleration due to gravity (g) = 10 m/s²
We know the formula of work, i.e., W = mgh
So, putting the values in the above formula, we get
W = 50 Kg × 75 m × 10 m/s²
or, W = 37500 J
Answer:
a. The Eiffel Tower is 300 m high.
b. The work done by Kate by climbing 400 steps is 37500 J.
Hope you could understand.
If you have any query feel free to ask.