Ted tells his incredulous nephews that he can turn a bucket of water upside down without the water pouring out! To illustrate, he puts a small amount of water in a bucket and swings it around in a circle so that the bucket travels from his knees, up over his head, and swings back down to his knees (see figure). If the water is 2.3 feet from the center of the circle of motion and is weightless at the top of the loop, what is the linear speed of the bucket? [Ignore the fact that the water in the bucket has depth; that is, pretend all the water is 2.3 feet from the loop's center.]
A) 8.6 ft/s
B) 3.7 ft/s
C) 4.3 ft/s
D) 17.2 ft/s

Question

Ted tells his incredulous nephews that he can turn a bucket of water upside down without the water pouring out! To illustrate, he puts a small amount of water in a bucket and swings it around in a circle so that the bucket travels from his knees, up over his head, and swings back down to his knees (see figure). If the water is 2.3 feet from the center of the circle of motion and is weightless at the top of the loop, what is the linear speed of the bucket? [Ignore the fact that the water in the bucket has depth; that is, pretend all the water is 2.3 feet from the loop's center.] 
A) 8.6 ft/s 
B) 3.7 ft/s 
C) 4.3 ft/s 
D) 17.2 ft/s

Quizplus · Accepted Answer

From the conservation of energy, at the top of the loop the potential energy of the water changes completely into kinetic energy. Therefore, we can write:

mgh = 1/2 mv^2

where m is the mass of the water, g is the acceleration due to gravity, h is the height above the ground (which we take to be 2.3 ft), and v is the linear speed of the bucket.

Solving for v, we get:

v = sqrt(2gh)

where sqrt denotes the square root.

Substituting the given values, we get:

v = sqrt(2 x 32.2 ft/s^2 x 2.3 ft)

v ≈ 8.6 ft/s

Therefore, the answer is A) 8.6 ft/s.

Ted Tells His Incredulous Nephews That He Can Turn a Bucket