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1) Your nephew rides a kiddy train at the local carnival. The train, which has
a mass of 1000 kg, rounds a curve with a radius of 5.0 m. The rails can
exert a maximum force of 2000 N in the radial direction. What is the
maximum speed of the train without derailing?

Respuesta :

nkirotedoreen46

Answer:

Velocity is 1 m/s

Explanation:

We are given;

  • Mass of the kiddy train is 1000 kg
  • Radius of the curve is 5.0 m
  • Centripetal force is 2000 N

We are required to determine the maximum speed of the train.

  • Centripetal force refers to the force experienced by an object in a circular motion towards the center of a circular path.
  • It is calculated by the formula;
  • [tex]Fc=\frac{Mv^{2} }{r}[/tex], where m is the mass, v is the velocity and r is the radius of the circular path.
  • Therefore, using the formula we can find the maximum speed.
  • Rearranging the formula;

[tex]v=\sqrt{\frac{Fc.r}{m} }[/tex]

  • Therefore;

[tex]v=\sqrt{\frac{(2000N)(5.0m)}{1000kg} }[/tex]

[tex]v=\sqrt{1}[/tex]

[tex]v=1m/s[/tex]

Therefore, the maximum speed of the train is 1 m/s

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