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Chapter 1: Q22E (page 391)

Two identical buckets are filled to the brim with water but one of them has a piece of wood floating in it. Which bucket of water weights more? Explain.

Short Answer

Expert verified

The weight of the bucket filled with water and the weight of the bucket containing the floating block is the same. As a result, the weight of both buckets is the same.

Step by step solution

01

Step:1 Given data

a) Two identical buckets were filled to the brim with water.

b) A piece of wood is found in one of the two buckets.

02

Step: 2 Principles and ideas

a) When a body is immersed in a fluid, the fluid exerts an upward force on the body, which is known as buoyant force. Therefore, when an object is displaced by a fluid, Archimedes鈥� principle states that its buoyant force is equal to the object's weight in fluid, such that

B=g脳脳pfluid脳Vdisplaced

b) Weight is the gravitational pull imposed on a body by the earth that determines its weight Weight is indeed a vector property. Gravitational acceleration (g) multiplied by the mass (m) of an object equals the magnitude of its weight (w) at any given point.

w=mg

03

Step: 3 Information that is required

We are asked to tell which of the two buckets weights more.

04

Solution

The weight of the bucket is can be written as:

w=pgV

Wherep is the density of water,V is the volume of water in a bucket

This demonstrates that the weight of the water is proportional to the amount of water in the bucket.

The water levels in both buckets are the same because a portion of the woodblock is visible above the surface of the water in both buckets. In line with Archimedes' principle, the floating block displaces a percentage of the volume of water equal to its weight when it is submerged. This kept the weight of the water in the bucket equal to the weight of the water in the other bucket.

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