A 240 g block on a 60 cm long string swings in circle on a horizontal, frictionless table at 95 rpm. What is the speed of the block? What is the tension of the string?
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> Let,
m = 240 g = 0.24 kg
L = 60 cm = 0.6 m
> Express the given angular velocity in radian/second ( rad/s).
`omega = 95 (rev)/min * (2pi rad)/(1 rev) *( 1 min)/(60 s)= 19/6 pi (rad)/s`
> Determine the weight of the block.
`W = mg = (0.24 kg)( (9.81 m/s) = 2.35 N`
> To solve for the tension (T) in the spring, consider the horizontal components of the forces acting on the block.
`sumF_x = 0`
`CF - Tcos theta = 0`
where, CF is the centrifugal force
`CF = (W/g )v^2/R = m v^2/R= m (omega R)^2/R = m omega^2R`
` cos theta = R/L`
(Note that R is the raduis of the circle formed by the rotating string.) ...
(The entire section contains 2 answers and 333 words.)
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