When you swing a bucket of water up and down in a vertical circle you can keep t

Question

When you swing a bucket of water up and down in a vertical circle you can keep the water in the bucket if you keep the velocity high enough. If you let the bucket slow down you get wet. The critical velocity is the slowest velocity necessary to keep the water in the bucket and not on you. What is the critical velocity for you if the formula is velocity = ?(rg) where the radius of your arm swing including the bucket is r and g is the acceleration of gravity? Hint: You must measure or estimate the length from your shoulder to the center of the bucket for the radius.

Explanation / Answer

What You Need small bucket with a handle or string attached water stopwatch meterstick person willing to get wet another person willing to get the first person wet optional: paper towels or a mop to wipe up spills optional: raincoat or umbrella Method Put some water in the bucket. Predict how fast you think you need to spin the bucket to avoid spilling its contents. This can be done qualitatively by spinning at a relatively fast rotation and pushing your luck by going progressively slower. One simple refinement would be to do this in terms of time (in seconds). A more quantitative prediction can be based on the linear or angular velocity, and it can be measured based on the person's arm length.) Spin the bucket, as shown in Figure 17-1, and evaluate in terms of the predictions. Expected Results The slower you go, the greater the risk of soaking the spinner for a given radius. If your arm is shorter, you will have to complete the circle in less time. The maximum time to go around a vertical circle of a given radius without spilling is shown in the table below. The maximum time to spin the bucket overhead is about half that time. Keep in mind these times are based on uniform velocity. The most critical point of course is at the top of the circle. (If you slow down there, you may need that raincoat identified in the what-you-need list.) Why It Works The person spinning the bucket will be spared a soaking as long as the bucket moves fast enough so the centripetal force is greater than the force of gravity. The condition for this is: Note, this result indicates it doesn't matter how much water is in the bucket as long as the spinner moves at a sufficient speed. The larger the radius, the faster you have to go. Too much water, however, may cause the spinner to slow down. Other Things to Try This can also be done using confetti instead of water. Physics alert: there is really no such thing as a centrifugal force. The water is given a velocity and is forced into a circular path by the centripetal force exerted by the bottom of the bucket on the water. If the bucket is moving fast enough, the centripetal force of the bucket is needed to keep it going in a circle. If the bucket is not going fast enough, gravity would be great enough to cause the water to spill out. The Point The centripetal force on the water is provided by the bottom of the bucket. The handle of the bucket provides a centripetal force on the bucket itself. The water will not fall if the rate of rotation is high enough that the centripetal force is at least as great as gravity.

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