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.
2 Answers
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Answers:
(a) Speed is 5.34 m/s
(b) Tension is 9.5 N
Method:
(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
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the angular speed is w=852pi/60 rad/s
the linear speed is w*r
and the force is m*r*w^2
