Centre of Mass/Tipping Point Question

In summary, the conversation suggests that the problem being discussed involves a bus being tested on a tilting ramp at an angle of 28 degrees from the vertical, not 10 degrees from the horizontal as initially interpreted. After re-calculating, the book answer of 2.3m is consistent with the calculated answer to 2 significant figures. It is believed that the discrepancy is due to a printing error.
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Homework Statement
The top deck of a bus is loaded with sandbags. The bus is tested to ensure all 4 wheels are in contact with the ground up, to at least 280 degrees to the vertical. The height of the bus is 4.4m and width is 2.4m. Calculate the height of the centre of mass of the loaded bus by assuming it would topple over at larger angles.
Relevant Equations
h = 1.2tan(10)
1653996533504.png

I drew out a small diagram to illustrate my attempt. I interpreted 280 degrees from the vertical as 10 degrees from the horizontal. Using trig I solved for the h, which I get an obviously incorrect answer. The actual answer in the book is 2.3m,
 
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  • #2
I suggest it means the bus base is tilted 10° to the horizontal.
 
  • #3
I believe that you have misread the question or that it has been poorly transcribed. It is not 280 degrees. It is 28 degrees (28°)

One can easily imagine a transcription error where a degree symbol is rendered as the digit zero.
https://www.quora.com/Why-do-double-decker-buses-not-tip-over said:
In the UK, British transportation regulations required that double decker buses be tested on a tilting ramp, to an angle of 28-degrees.
Note that this is 28 degrees from the vertical, not 10 degrees from the horizontal. So the relevant formula will change slightly from the one you have used.

With those tweaks in mind, I get the book answer to two significant digits.

Edit to add graphical image
https://www.ltmuseum.co.uk/collections/collections-online/photographs/item/2002-18969 said:
1654008667895.png
 
Last edited:
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  • #4
jbriggs444 said:
I believe that you have misread the question or that it has been poorly transcribed. It is not 280 degrees. It is 28 degrees (28°)

One can easily imagine a transcription error where a degree symbol is rendered as the digit zero.

Note that this is 28 degrees from the vertical, not 10 degrees from the horizontal. So the relevant formula will change slightly from the one you have used.

With those tweaks in mind, I get the book answer to two significant digits.
Thank you, after re-calculating I get 2.256..., which is consistent with the answer to 2.s.f. It unfortunately appears to be a printing error.
 
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Related to Centre of Mass/Tipping Point Question

1. What is the Centre of Mass/Tipping Point Question?

The Centre of Mass/Tipping Point Question is a physics concept that deals with the balance and stability of an object. It refers to the point at which the weight of an object is evenly distributed, causing it to remain in a stable position.

2. How is the Centre of Mass determined?

The Centre of Mass is determined by calculating the average position of all the mass in an object. This can be done by dividing the total mass of the object by the sum of all its individual masses multiplied by their respective distances from a chosen reference point.

3. What factors can affect the Centre of Mass of an object?

The Centre of Mass of an object can be affected by its shape, size, and distribution of mass. Any changes in these factors can shift the Centre of Mass and potentially affect the stability of the object.

4. How does the Centre of Mass relate to an object's stability?

The Centre of Mass is directly related to an object's stability. If the Centre of Mass is located within the base of support, the object will remain stable. However, if the Centre of Mass is located outside the base of support, the object will become unstable and may tip over.

5. Can the Centre of Mass be outside of an object?

Yes, the Centre of Mass can be outside of an object. This is often the case with irregularly shaped objects or objects with uneven mass distribution. In these cases, the object's stability may be compromised, and it may be more likely to tip over.

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