Question

A rock with a 8 kg mass is tied to a string and swung in a circular path. The 1.8 meter string is tied to a post, and during the motion, the string has a 35° angle with the post. The rock makes 100 rounds in 3 minute. The centripetal force on the ball is __ N.

Answer 1

The centripetal force of the rock tied to a string and swung in a circular path is determined as 1.65 N.

Angular speed of the rock

The angular speed of the rock is calculated as follows;

ω = 2π N

$\omega = 35^0 \times \frac{2 \pi \ rad}{360^0} \times \frac{100}{3\min} \times \frac{1 \min}{60 \ s} \\\\\omega = 0.339 \ rad/s$

Centripetal force of the rock

The centripetal force of the rock is calculated from the product of mass and centripetal acceleration as shown below;

Fc = ma

Fc = m(ω²r)

Fc = mω²r

Fc = 8 x (0.339)² x 1.8

Fc = 1.65 N

Thus, the centripetal force of the rock tied to a string and swung in a circular path is determined as 1.65 N.

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