Question

A beaker is filled with water to the rim. Gently placing a plastic toy duck in the beaker causes some of the water to spill out. The weight of the beaker with the duck floating in it is a) greater than the weight before adding the duck. b) less than the weight before adding the duck. c) the same as the weight before adding the duck. d) greater or less than the weight before the duck was added, depending on the weight of the duck.

Short answer

Answer: c) The same as the weight before adding the duck.

Step-by-step solution

Identify the important factors in the problem

To find the weight of the beaker with the duck floating in it, we need to consider the following factors: - the weight of the water-filled beaker before adding the duck (W1) - the weight of the duck (W2) - the weight of the water displaced by the duck (W3)

Apply Archimedes' Principle

Archimedes' Principle states that the buoyant force on a submerged or floating object is equal to the weight of the fluid displaced by the object. In this case, the duck floats in the water, so the buoyant force (Fb) is equal to the weight of the water displaced by the duck: Fb = W3

Calculate the weight of the beaker with the duck floating in it

To find the weight of the beaker with the duck floating in it (W4), we need to consider the weight of the beaker with water before adding the duck (W1), the weight of the duck (W2), and the weight of the water displaced by the duck (W3): W4 = (W1 - W3) + W2 Since the buoyant force (Fb) is equal to the weight of displaced water (W3) and is also equal to the weight of the duck (W2) when it is floating: W4 = (W1 - Fb) + Fb W4 = W1

Compare the weights

Comparing the weight of the beaker with the duck floating in it (W4) to the weight of the beaker before adding the duck (W1), we find they are equal: W4 = W1

Select the correct answer

Based on our calculations, the weight of the beaker with the duck floating in it is the same as the weight before adding the duck. So, the correct answer is: c) the same as the weight before adding the duck.

Key concepts

Buoyant Force

Understanding the concept of buoyant force is fundamental when tackling problems related to objects submerged in a fluid, such as water. When an object is placed in a fluid, it experiences an upward force that opposes the weight of the object — this is known as the buoyant force. According to Archimedes' Principle, this force is equivalent to the weight of the fluid that the object displaces.

Consider a plastic toy duck floating in a beaker of water. The water pushes up against the duck with a force equal to the weight of the water that would otherwise fill the space occupied by the duck. The duck feels lighter in the water precisely because of this force. In practical problem solving, one must always ensure that the principle is properly applied by equating the buoyant force to the weight of the displaced fluid. This is crucial because it allows us to predict and explain the floating or sinking behavior of objects.

Moreover, if the object is floating and at rest, the buoyant force is balanced by the object's weight, leading to the floating condition where the two forces are equal. This equalizing effect is useful for calculating the changes in overall system weight, as seen in the exercise with the duck and beaker.

Fluid Displacement

The term fluid displacement refers to the phenomenon that occurs when an object is immersed into a fluid, causing the fluid to move and make room for the object. The amount of fluid displaced is directly related to the volume of the object submerged. In the case of our exercise involving the plastic toy duck, when the duck is gently placed into a full beaker of water, it displaces an amount of water equivalent to its own volume.

Understanding fluid displacement is key to solving many physics problems, especially those related to buoyancy. If planned adequately, the concept can illustrate why some things float and others sink, depending on the density difference between the object and the fluid. For objects that float, like the duck, the weight of the displaced water equates to the weight of the object itself (Archimedes' Principle). This leads to interesting consequences, such as the fact that even heavy ships can float on water as long as they displace a sufficient volume of water to balance their weight.

In our textbook problem, the fluid displacement also implicitly confirms that the weight of the beaker remains unchanged after the duck is added. This is because the weight of the displaced water, which spills out, is exactly equal to the weight of the duck that takes its place.

Physics Problem Solving

Successful physics problem solving requires a systematic approach that combines an understanding of relevant physical principles with a logical method for applying them to specific scenarios. The steps in solving the exercise provided serve as a template for addressing similar problems in a clear and coherent manner.

Firstly, identify the key factors and variables involved in the problem. Here, we considered the weight of the beaker before and after the duck was placed in it, the buoyant force, and the weight of the displaced water. Next, apply the fundamental principles of physics that relate to the problem; in our case, we used Archimedes' Principle to relate the buoyant force to the weight of the displaced water.

Then, through mathematical reasoning, we can solve for the unknown quantities. Keeping the process transparent and showing all steps ensures that it is not only easy to follow but also allows for a better grasp of the concepts at play.

Finally, reflecting on the solution to understand the result and confirm it against physical intuition is crucial. For example, realizing that the total weight of the beaker system remains the same before and after the duck is added, despite the presence of the duck, instills a deeper understanding of the principles of buoyancy and fluid displacement.