*dot*--------------------------------------------> Radius of Curvature=100m ----
ID: 2099773 • Letter: #
Question
*dot*--------------------------------------------> Radius of Curvature=100m --------------> bank with car at 4.0 degrees -
*center of Curvature*
A car rounds a reserved bank curve. The radius of curvature of the road, R, is 100m, the banking angle,theta 4.0 degrees and the coefficient of static friction, (M,s) is 0.1.00
A. Determine the minimum speed the car must have to avoid slipping down the bank.
B. Is there a speed such that the car will slip up the bank?
(Explain your answewr quantitatively using free body diagrams and Newtons second Law)
Explanation / Answer
theta =4
At minimum speed the force of friction just balances the weight component and centripetal force
u*m*g*cos heta=m*g*sin theta+m*V^2/R
cancelling m out
V=sqrt((-sintheta+u*cos theta)*r*g)=5.477m/sec
B)Yes there is such speed so that if vehicle speed crosses the specified speed the car will slip up the bank
In that case,the centrifugal force crosses the combined force of weight component and friction bboth acting downwards
Both are constant(depends on banking angle)and cannot be increased.So if velocity crosses a particular limit the surface wont be able to hold the vehicle and it topples up
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