A 200g block on a 60.0cm -long string swings in a circle on a horizontal, frictionless table at 85.0rpm.
(a) What is the speed of the block?
(b) What is the tension in the string?
Express your answer with the appropriate units.
(a) Speed is 5.34 m/s
(b) Tension is 9.5 N
(a) speed = distance / time
The distance is the circumference = 2πr = 2 x 3.14 x 0.6 m = 3.77 m
The time is the period =1/frequency = 1/85/min = 60 sec / 85 = 0.706 s
Substituting: speed = distance / time = 3.77 m / 0.706 s = 5.34 m/s
(b) The tension is the centripetal force = mv^2 / r = 0.2 kg x (5.34 m/s)^2 / 0.6 m = 9.5 N
the angular speed is w=852pi/60 rad/s
the linear speed is w*r
and the force is m*r*w^2