- #1
ixerr
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Homework Statement
For some reason, I keep getting this problem wrong, could someone please look over it and tell me what I am doing incorrectly? Here it is:
A student ties a 410.0 g rock to a 1.25 m-long string and swings it around her head in a horizontal circle. At what angular speed (in rev/min) does the string tilt down at a 13.9° angle, assuming that the local acceleration due to gravity is -9.80 m/s^2?
Homework Equations
Force centripetal = (mass*velocity) / radius
The Attempt at a Solution
To support the 0.410 kg rock at an angle of 13.9° angle below horizontal,
the vertical component of the tension in the string must equal the weight of the rock
weight of rock = 0.410 * 9.8 = 4.018 N
Vertical component of tension = T * sin 13.9°
T * sin 13.9° = 4.018 N
T = 16.726 N
The horizontal component of the tension is the Force centripetal
The horizontal component of the tension = T * cos 13.9° = 16.726 N
Force centripetal = (mass * velocity^2) / radius
16.236 = 0.41 * v^2 / 1.25
v = 7.036 m/s
1 radian = 1.1 m
Angular velocity = 6.396 rad/s