Question

A boat can safely displace 2.50 m3 of water without sinking, and the boat itself has a mass of 850 kg. What maximum mass of passengers and cargo can the boat carry safely in a fresh-water lake? [6] 2.2 A pipe in the basement of an apartment complex is accidentally punctured, causing a leak through the small hole formed (see Figure 2). An astute physics student estimates that the water is leaking out a speed of 25 m/s. Apply the Bernouli equation to estimate the gauge pressure inside the pipe. [8]

Answer 1

The boat will go under water when its total density is close to the density of water, therefore we have:

$$(m_{boat}+m_{cargo})/V=\rho_{water}$$

$$m_{cargo}=\rho_{water}*V-m_{boat}$$

$$m_{cargo}=1650kg$$

According to Bernoulli’s law, dynamic pressure equals:

$$p=\rho*V^2/2=1000*625/2=312500Pa$$

Answer: 1650 kg, 312.5kPa