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The 1kg rock is tied to a string and swung in a circular path as shown. The 1 meter string is tied to a post, and during the motion, the string has a 30 angle with the post. The rock makes 100 rounds in 1 minute. The centripetal force on the rock is

Respuesta :

Answer: 54.8

Explanation:

onyebuchinnaji

The centripetal force on the rock moving along the string is 104.66 N.

The given parameters;

  • the mass of the rock, m = 1 kg
  • angle of inclination of the string, θ = 30⁰
  • angular velocity of the rock, ω = 100 rev/min
  • length of the string, r = 1 m

The centripetal acceleration of the rock is calculated as follows;

[tex]\omega _f^2 = \omega _i^2 + 2\alpha (\theta)\\\\(100 \ \frac{rev}{\min} \times \frac{2\pi \ rad}{1 \ rev} \times \frac{1 \min}{60 \ s} )^2 = 0 + 2\alpha (30 ^0 \times \frac{\pi \ rad}{180^0} )\\\\109.69 = 1.048\alpha \\\\\alpha = \frac{109.69}{1.048} \\\\\alpha =104.66 \ rad/s^2[/tex]

[tex]a_c = \alpha \times r\\\\a_c = 104.66 \times 1 = 104.66 \ m/s^2[/tex]

The centripetal force on the rock is calculated as follows;

[tex]F_c = ma_c[/tex]

[tex]F_c = 104.66 \times 1\\\\F_c = 104.66 \ N[/tex]

Thus, the centripetal force on the rock moving along the string is 104.66 N.

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