A ball of mass 500g attached to a light inextensible strings whirled around at a constant speed of 8m/s. If the tension necessary to maintain the body in circular motion is 80.0N, calculate the length of the string.
f = m v^2 / r
r = m v^2 / f
To find the length of the string, we can use the centripetal force formula:
F = (m * v^2) / r
Where:
F = Centripetal force (tension in the string) = 80.0 N
m = Mass of the ball = 500 g = 0.5 kg
v = Speed of the ball = 8 m/s
r = Length of the string (radius of the circular path)
We can rearrange the formula to solve for r:
r = (m * v^2) / F
Substituting the given values into the formula, we get:
r = (0.5 kg * (8 m/s)^2) / 80.0 N
r = (0.5 kg * 64 m^2/s^2) / 80.0 N
r = 32 m^2/(kg⋅s^2) / 80.0 N
r = 0.4 m
Therefore, the length of the string is 0.4 meters.