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The combined mass of a race car and its driver is 600 kg. Travelling at constant speed, the car completes one lap around a circular track of radius 160 m in total time of 36 s. What is the magnitude of the centripetal acceleration of the car?​

Respuesta :

quasarJose

Answer:

4.88m/s²

Explanation:

Given parameters:

 Mass of the race car and driver = 600kg

  Radius of path = 160m

   time taken  = 36s

Unknown:

Centripetal acceleration  = ?

Solution:

The centripetal acceleration is the change in velocity of a body along a circular path with time.

It is mathematically expressed as;

         a = [tex]\frac{v^{2} }{r}[/tex]  

v is the velocity

r  = radius of path

           v  = [tex]\frac{2\pi r}{t}[/tex]  

  t is the time;

   Insert the parameters and solve for the velocity;

          v  = [tex]\frac{2 x \pi x 160}{36}[/tex]   = 27.9m/s

Now,

         acceleration  = [tex]\frac{27.9^{2} }{160}[/tex]    = 4.88m/s²

snehashish65

The magnitude of the centripetal acceleration of the car is [tex]4.87 \;\rm m/s^{2}[/tex].

Given data:

The combined mass of race car and its driver is, m = 600 kg.

The radius of the circular track is, r = 160 m.

The time taken to cover one lap is, t = 36 s.

The velocity of the car while covering one complete lap of circular track is given as,

[tex]v = \dfrac{2 \pi r}{t}\\\\v = \dfrac{2 \pi \times 160}{36}\\\\v = 27.92 \;\rm m/s[/tex]

And the expression for the magnitude of centripetal acceleration is given as,

[tex]a=\dfrac{v^{2}}{r}\\\\a=\dfrac{27.92^{2}}{160}\\\\a=4.87 \;\rm m/s^{2}[/tex]

Thus, we can conclude that the magnitude of the centripetal acceleration of the car is [tex]4.87 \;\rm m/s^{2}[/tex].

Learn more about the centripetal acceleration here:

https://brainly.com/question/6082363

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