a 2.25 kg bucket of water attached to a rope is swung in a 0.809 m circle. At the top the tension in the rope is 15.5 N

To determine the speed of the bucket at the top of the swing, we can use the centripetal force equation:

F = m * v^2 / r

Where:
F is the force (tension in the rope) = 15.5 N
m is the mass of the bucket = 2.25 kg
v is the speed
r is the radius of the circular path = 0.809 m

Rearranging the equation, we can find the speed v:

v = √(F * r / m)

Substituting the given values:

v = √(15.5 N * 0.809 m) / 2.25 kg

Calculating further:

v = √(12.5745 N*m) / 2.25 kg

v = √(5.587333333 m^2/s^2) / 2.25 kg

v = √(2.482035087 m^2/s^2) / 2.25 kg

v = 1.575 m/s

Therefore, the speed of the bucket at the top of the swing is approximately 1.575 m/s.

fascinating ... really ...