Final answer:
The minimum velocity the bucket must have to make it around the top of the circle is approximately 3.92 m/s.
Step-by-step explanation:
To determine the minimum velocity the bucket must have to make it around the top of the circle, we can use the concept of centripetal force.
The centripetal force is given by the equation F = m * v^2 / r, where F is the centripetal force, m is the mass of the bucket, v is the velocity, and r is the radius of the circle.
At the top of the circle, the centripetal force is equal to the weight of the bucket, which is given by the equation F = m * g, where g is the acceleration due to gravity.
Setting the centripetal force equal to the weight of the bucket, we have m * v^2 / r = m * g. Rearranging the equation, we find v = sqrt(r * g).
Plugging in the values for r = 0.80 m and g = 9.8 m/s^2, we get v = sqrt(0.80 * 9.8) = 3.92 m/s.
Therefore, the minimum velocity the bucket must have to make it around the top of the circle is approximately 3.92 m/s.