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muminat
2 years ago
7

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the ro

ad is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?
Physics
1 answer:
Vlada [557]2 years ago
6 0

To solve this problem it is necessary to take into account the concepts related to Centripetal Force and Friction Force.

In the case of the centripetal force, we know that it is defined as

F_c = \frac{mv^2}{R}

Where,

m=mass

v= velocity

r= Radius

In the case of the Force of Friction we have to,

F_f = \mu m*g

Where,

\mu =Friction Constant

m= mass

g= gravity

According to the information given, the centripetal force must be less than or equal to the friction force to stay on the road, in this way

\frac{mv^2}{R} \leq \mu m*g

Re-arrange to find the velocity,

v \leq \sqrt{\mu gR}

v \leq \sqrt{(0.6)(9.8)(300)}

v \leq 42m/s

Therefore la velocidad del carro debe ser igual o menor a 42m/s para mantenerse en el camino

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Answer: 0.13m/s^2

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We have an object whose position r is given by a vector, where the components X and Y are identified by the unit vectors i and j (where each unit vector is defined to have a magnitude of exactly one):

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On the other hand, velocity is defined as the variation of the position in time:

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This means we have to derive r:

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\frac{dr}{dt}=(2 m/s) i - (\frac{1}{2} m/s^{2} t) j This is the velocity vector

And when t=2s the velocity vector is:

\frac{dr}{dt}=(2 m/s) i - (\frac{1}{2} m/s^{2} (2 s)) j

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However, the solution is not complete yet, we have to find the module of this velocity vector, which is the speed S:

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