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.