Answer to Question #170914 in Physics for Brandon

Question

During his lab exercise, Jens measured that the density of a piece of wood was p= 740kg / m³. The analysis of his results showed that the accuracy of the measurement was approx ±30 Kg / m³. Before the summer, you will build a fleet of the same type of wood that Jens measured in the lab. The fleet must be able to float in the water with you, three friends, a tent, and other equipment totaling 600kg (including people). To be able to do this without too great risks for the fleet's rollover, the fleet must not start to sink before it is loaded with at least 2600 kg.

How much should the fleet itself weigh?

 

Answer 1

$$\rho _w gV=mg+F\\ F=\left(\frac{\rho_w}{\rho}-1\right)W\\ 2600=\left(\frac{1000}{740}-1\right)m\\m=7400\ kg$$