A 2.00-kg stone attached to a rope 4.00 m long is whirled in a circle horizontally on a
frictionless surface, completing 5.00 revolutions in 2.00 s. Calculate the magnitude of
tension in the rope.
The centripetal force acting on the stone is provided by the tension in the rope. The centripetal force can be calculated using the formula:
F = (m*v^2) / r
Where:
F = centripetal force
m = mass of the stone = 2.00 kg
v = tangential speed = (2πr*5) / t = (2π*4*5) / 2 = 20π m/s
r = radius of the circle = 4.00 m
Now, we can calculate the centripetal force:
F = (2.00 * (20π)^2) / 4.00
F = 800π^2 N
Therefore, the magnitude of tension in the rope is equal to the centripetal force:
T = 800π^2 N
T ≈ 2500 N