Question

Henry Ford College Physics 231-02 Spring 2017 Problem 3 (25 points) a) An object of mass m swings in a horizontal circle on the string of length L that tilts downward at angle Find an expression for the angular velocity ay head in a horizontal circle. b) A student a 250 g rock to a 80 cm-long string and swings it her around ties a down at 10e angle? At what angular speed, in rpm, does the string tilt c) what is the object's centripetal force and acceleration when the string tilts down at 10° angle?

Answer 1

T cos theta = mg ---- (1) T sin theta = mw^2r -------(2) w^2r/g = tan theta Also, r = l sin theta w^2 l sin theta/g = tan theta w^2l/g = 1/ cos theta w = squareroot g/l cos theta For theta = 10 degree w = squareroot 9.81/0.80 times cos 10 degree = 3.52 rad s^-1 centripetal force mw^2r = 0.25 times 3.52^2 times 0.80 times sin 10 degree = 0.13N acceleration = w^2r = 1.72m/s^2