Chapter 8, Problem 14TE

A half-filled bucket of water is on a spring scale. Will the reading of scale increase or remain the same if a fish is placed in the bucket? Will your answer be different if the bucket is initially filled to the brim?

To determine

The effect on the reading of the spring scale due to placing the fish in the half filled bucket of water and whether the answer is different for initially filled brim in the bucket.

Answer to Problem 14TE

The reading of the spring scale increases in the half-filled bucket due to an increase in the weight of the bucket and remains same in the bucket initially filled to the brim because the volume of water equal to weight of the fish overflows from the bucket.

Explanation of Solution

The reading of a spring scale is same as the force exerts on the spring scale. If the force on the spring varies, then the readings of the spring scale also vary.

The reading of the half-filled bucket on the spring scale is same as the weight of the water in the bucket. When a fish is placed in the half-filled bucket, then the weight of the bucket increased. The reading of the spring scale increase due to an increase in the weight of the bucket.

If the bucket is initially filled to the brim, then the water from the bucket flows out due to water displaced equal to the weight of the fish. The reading of the spring scale remains same if the fish is placed in the bucket that is initially filled to the brim.

Conclusion:

Therefore, the reading of the spring scale increases in the half-filled bucket due to an increase in the weight of the bucket and remains same in the bucket initially filled to the brim because the volume of water equal to weight of the fish overflows from the bucket.