Question 3 4 marks in totall Suppose that a new gym is looki

Question 3 [4 marks in totall Suppose that a new gym is looking to rent one floor from a 5-storey building (ground floor floor 0, and then there are upper floors 1 5). The building has floors 1,2 and 3 available to lease. Each floor of the building is 5 metres apart. The owner of the building has studied as a civil engineer and is concerned that the vibrations on the support beams caused by heavy weights being dropped will disturb the other tenants. After some experiments by dropping objects of varying weights, the building owner concluded that the average deviation of a support beam from the vertical is 0.0033 radians.

Solution

solution

If a heavy object is dropped it puts stress on the beams and they move sideways by a tiny bit.

The floor below will be impacted by

Tan (0.0033 radians) = x/5 metres

x=5tan(0.0033)

x=0.0165m

x=16.5mm (That seems a lot)

2 floors below will be impacted 33mm

3 floors below will be impacted 3*16.5=49.5mm

b) I\'m even less sure here ...... maybe ....

There are 4 floors between the 1st and the fifth so maybe it is just 4*16.5 = 66mm etc.