uniform circular motion

2010-07-25 11:23 pm
A bus turns a corner with a radius of curvature of 18m on a banked road. The coefficient of the friction u for its tyre on the road is 0.8. The bus initially moves in a uniform circular motion and it starts to change its speed.

a)At what speed would the bus start to skid outwards?

b)At what speed would the bus start to overturn inwards?

c)What is the range of the speedfor turning this corner safely?

回答 (1)

2010-07-26 12:51 am
✔ 最佳答案
Let u=tanλ, see te figure for analysis

圖片參考:http://imgcld.yimg.com/8/n/HA00140412/o/701007250069613873372098.jpg


2010-07-25 16:57:35 補充:
(a)
At what speed would the bus start to skid outwards?
v^2 = grtan(θ+λ)

(b)
At what speed would the bus start to overturn inwards?
v^2=grtan(θ-α)

It is very rare to overturn inwards(as I have mention, it is because if that happens the bus will even topple when it is at rest on the banking)

2010-07-25 16:57:39 補充:
I guess you ask at what speed would the bus start to verturn outwards( i.e. away from centre)
v^2=grtan(θ+α)

2010-07-25 16:57:46 補充:
(c)
What is the range of the speedfor turning this corner safely?
See above

Note that
α is the angle between the vertical and the symmetry axis about the bus,
α = a/h
h = height of CG above the ground.

2010-07-25 17:00:26 補充:
Your qestion don't give enough information to get the exact anumerical answer.
This time you miss out:
The angle of banking
The geometry of the bus(e.g. height of CG, distance between two pairs of wheel)


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