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Romashka [77]
3 years ago
14

Determine the minimum angle at which a frictionless road should be banked so that a car traveling at 20.0 m/s can safely negotia

te the curve if the radius of the curve is 200.0 m.

Physics
1 answer:
EleoNora [17]3 years ago
3 0

Answer:

Minimum angle at which frictionless road should be banked is 11.53°

Explanation:

Consider the figure below to understand the banking curve. θ is  minimum angle at which frictionless road should be banked.

Forces acting along x-axis:

F_{N}sin\theta=\frac{mv^{2}}{R}---(1)\\\\

Forces acting along y-axis:

F_{N}cos\theta-mg=0---(2)\\\\

Dividing (1) and (2)

\frac{F_{N}sin\theta}{F_{N}cos\theta}=\frac{\frac{mv^{2}}{R}}{mg}\\\\tan\,\theta=\frac{v^{2}}{rg}\\\\v=20\,m/s,\,r=200\,m\\\\tan\,\theta=\frac{(20)^{2}}{(200)(9.8)}\\\\tan\,\theta=0.204\\\\\theta=tan^{-1}(0.204)\\\theta=11.53^{o}\\

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3 years ago
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A small branch is wedged under a 200 kg rock and rests on a smaller object. The smaller object is 2.0 m from the large rock and
Alexxandr [17]

Answer:

a

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b

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Explanation:

From the question we are told that

          The mass of the rock is  m_r  =  200 \ kg

          The  length of the small object from the rock is  d  =  2 \ m

          The  length of the small object from the branch l  =  12 \ m

An image representing this lever set-up is shown on the first uploaded image

Here the small object acts as a fulcrum

The  force exerted by the weight of the rock is mathematically evaluated as

      W =  m_r *  g

substituting values

     W =   200 *  9.8

     W =   1960 \ N

 So  at  equilibrium the sum  of the moment about the fulcrum is mathematically represented as

         \sum  M_f  =  F * cos \theta *  l  -  W cos\theta  *  d =  0

Here  \theta is very small so  cos\theta  *  l  =  l

                               and  cos\theta  *  d  =  d

Hence

       F *   l  -  W  * d =  0

=>    F  = \frac{W * d}{l}

substituting values

        F  = \frac{1960 *  2}{12}

       F  =326.7 \ N

The  mechanical advantage is mathematically evaluated as

          M  = \frac{W}{F}

substituting values

        M  = \frac{1960}{326.7}

       M  = 6

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