Question

you are participating in a fresh water fishing tournament with the goal of catching the heaviest fish. you are in the middle of the river when you finally get your catch; unfortunately, you realize that you left the spring scales in your car. all you have in the boat are the paddles, your 16 oz coffee mug, some rope, measuring tape, and a plastic bag. estimate the mass of the fish (in kilograms) using these items.

Explanation:

Step1: Use the coffee mug as a measuring tool

First, fill the coffee mug with water. Since \(1\space oz = 0.0295735\space L\), a \(16 - oz\) mug has a volume \(V=16\times0.0295735 = 0.473176\space L\). The density of water \(
ho = 1\space kg/L\), so the mass of water in a full - mug \(m_{water}=
ho V= 0.473176\space kg\)

Step2: Create a balance

Tie the rope to the middle of a paddle to create a balance (a lever). Hang the plastic bag (to hold the fish) on one end of the paddle and the coffee mug (which can be filled with water multiple times) on the other end.

Step3: Calibrate the balance

Add water to the mug in increments (e.g., half - mug, full - mug) and see how much “counter - mass” (in terms of water - filled mugs) is needed to balance the fish. Let's say it takes \(n\) full mugs (or equivalent fractions of mugs) of water to balance the fish.

Step4: Calculate the mass of the fish

The mass of the fish \(m_{fish}=n\times m_{water}\). For example, if it takes \(3\) full mugs of water to balance the fish, then \(m_{fish}=3\times0.473176 = 1.419528\space kg\)

Answer:

The mass of the fish \(m_{fish}=n\times0.473176\space kg\), where \(n\) is the number of \(16 - oz\) (equivalent in water - mass) needed to balance the fish on the paddle - rope balance.