- #1
TonkaQD4
- 56
- 0
A boy ties a 500kg rock to a 1.0m long string and swings it around his head in a horizontal circle. At what angular velocity, in rpm, does the string tilt down at a 10 degree angle?
sintheta = mg / T
sin10 = 0.5kg(9.8m/s^2) / T
T = 4.9N / sin10
T = 28.22N
THEN...
v = SqRt [(rTcostheta) / m] ---> However the radius of the circle is not the length (L) so, r = Lcostheta
v = SqRt [(LTcos^2 theta) / m]
v = SqRt [(1.0m)(28.22N)(cos10^2) / 0.5kg]
v = 7.4m/s
FINALLY...
OMEGA = v / r
= v / Lcostheta
7.4rad / 1sec x 1rev / (2pi)rad x 60sec / 1 min --> rad and sec cancel out, leaving...
= 70.7 rpm
This was my initial attempt to the problem but I am not sure if everything is correct?
sintheta = mg / T
sin10 = 0.5kg(9.8m/s^2) / T
T = 4.9N / sin10
T = 28.22N
THEN...
v = SqRt [(rTcostheta) / m] ---> However the radius of the circle is not the length (L) so, r = Lcostheta
v = SqRt [(LTcos^2 theta) / m]
v = SqRt [(1.0m)(28.22N)(cos10^2) / 0.5kg]
v = 7.4m/s
FINALLY...
OMEGA = v / r
= v / Lcostheta
7.4rad / 1sec x 1rev / (2pi)rad x 60sec / 1 min --> rad and sec cancel out, leaving...
= 70.7 rpm
This was my initial attempt to the problem but I am not sure if everything is correct?