# Archimedes principle, bernoulli's equation

#### Lalasushi

hey can any1 help me with these 3 questions?

1. a piece of lead has a shape of a hockey puck with a diameter of 7.5cm and a height of 2.5cm. If the puck is placed in a mercury bath it floats. how deep below the surface of the mercury is the bottom of the lead puck? [2.1cm]

(can anyone give me some starters help with this, like guide me in the right direction becuase im really clueless about this one)

2. a garden hose is attached to a water faucet on one end and a spray nozzle on the other end. The water faucet is turned on but the nozzle is turned off so that no water flows through the hose. The hose lies horizontally on the ground and a stream of water sprays vertically out of a small leak to a hieght of 0.75m. What is the pressure inside the hose? [ans: 7.4kPa]

(i really have absolutely no idea with this because this is to do with bernoulli's equation but i really still don't have a clue)

3. A 0.12kg balloon is filled with helium (density = 0.719kg/m^3). if the balloon is a sphere with a radius of 5.2m, what is the maximum weight it can lift? [ans: 5.7kN]

(with this question, i tried finding the mass of the inside of the balloon by m = density x volume...where density = 0.179, and volume = 4/3 pi r^3...where r = 5.2...and my answer came out to be 105.43kg...multiplying that by 9.8 but that does not give me the right answer...so can anyone see what im doing wrong?)

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#### arildno

Homework Helper
Gold Member
Dearly Missed
Let's take 1.
a) What forces act upon the hockey puck in the equilibrium position?
b) If you designate the unknown penetration depth with "h", what equation for "h" does a) give you?
(Penetration depth is how deep the puck sticks down beneath the fluid surface in the equilibrium position.)

#### HallsofIvy

Homework Helper
I'm not sure you need to look at forces themselves. Archimedes principle says that a solid will sink into a liquid until the it displaces a volume of the liquid that has the same weight as the solid. Lead will float on mercury because lead has a lower density than mercury (is that true?). Okay, what is the mass of this piece of lead? What volume of mercury has that same mass? Assuming a cylinder of radius the same as the lead, what height will give you that volume?

#### arildno

Homework Helper
Gold Member
Dearly Missed
Well, I think the OP has trouble with stating/applying Newton's 2.law to start with.
That's rather troublesome.

That's why I chose to focus in on that approach.

But, different valid perspectives is hopefully to the benefit of OP.

#### OlderDan

Homework Helper
Lalasushi said:
3. A 0.12kg balloon is filled with helium (density = 0.719kg/m^3). if the balloon is a sphere with a radius of 5.2m, what is the maximum weight it can lift? [ans: 5.7kN]

(with this question, i tried finding the mass of the inside of the balloon by m = density x volume...where density = 0.179, and volume = 4/3 pi r^3...where r = 5.2...and my answer came out to be 105.43kg...multiplying that by 9.8 but that does not give me the right answer...so can anyone see what im doing wrong?)
It's a small effect, but don't forget the mass of the balloon itself when you calculate the weight of the balloon. Have you calculated the weight of the air displaced by the balloon?

#### Lalasushi

thanks for the 1st question guys. im still having trouble with getting the right answer for the 3rd question because i found the weight of air displaced by the balloon but the problem is that even if I did add the mass of the balloon itself, my answer is still 5 fold smaller than the right answer. what can i possibly be doing wrong?!?!

#### OlderDan

Homework Helper
Lalasushi said:
thanks for the 1st question guys. im still having trouble with getting the right answer for the 3rd question because i found the weight of air displaced by the balloon but the problem is that even if I did add the mass of the balloon itself, my answer is still 5 fold smaller than the right answer. what can i possibly be doing wrong?!?!
You have two very different numbers in your original post for the density of helium. It looks like you are using the larger one, which is incorrect. The mass of 0.12kg for the bolloon seems unrealistic. Using that number I get an answer that is larger than your posted answer by an amount that could easily be fixed with a realistic value for balloon mass. 72kg would do it. Check your numbers.

There is also some variation in published numbers for the density of air. What does your book say?

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