Mass propelled backwards in 1 second?

[ultralightbeam]

Homework Statement

Cross sectional area: 4.5x10^-2 m
Speed: 3.5ms-1
Density of sea water: 1030 kg m-3

Calculate the mass of water propelled backwards in 1 s.

Homework Equations

The Attempt at a Solution

Could someone just guide me through it, maybe give me a starting point like which equation to use...Im unsure how to do this?

My thought was that its related to the power equation?

 

[gneill]

Cross sectional area of what? Speed of what?

You need to provide a clear description of the problem.

 

[ultralightbeam]

Sorry, first post on here.

The motor on a small boat has a propeller attached that sends back a column of warer of cross-sectional area 4.5x10^-2 m^2 at a speed of 3.5ms. Density of seawater: 1030 kgm3
water is originally at rest

 

[SophiaSimon]

What is the context of the problem?

 

[ultralightbeam]

What is the context of the problem?

Added it as a reply.

 

[SophiaSimon]

:) Just slow.

First, how much distance does any cross-sectional area of water cover in 1s if it is traveling at $3.5\frac{m}{s}$?

 

[berkeman]

cross-sectional area 4.5x10^12 m^2

That's got to be a typo...

 

[ultralightbeam]

That's got to be a typo...

Yes it is, sorry I am pretty clumsy on the keyboard.

4.5x10^-2

 

[gneill]

Make yourself a drawing. Imagine a tube of water with your given cross sectional area moving at velocity v. Find the amount of water that moves past a given "starting line" in one second:

 

[ultralightbeam]

Make yourself a drawing. Imagine a tube of water with your given cross sectional area moving at velocity v. Find the amount of water that moves past a given "starting line" in one second:

View attachment 98816

So would that just be the cross-sectional area multiplied by 3.5 since the velocity is 3.5 metres per second? Giving a value of 0.1575m^3

 

[gneill]

Don't forget to include the time (1 s). It's important to make the units come out right. You should always check that the units come out right!

How are you going to convert that volume of water to a mass value?

 

[ultralightbeam]

Don't forget to include the time (1 s). It's important to make the units come out right. You should always check that the units come out right!

How are you going to convert that volume of water to a mass value?

Would you divide it by the time so 1second? Since the question asks the mass in 1 second?

 

[gneill]

Would you divide it by the time so 1second? Since the question asks the mass in 1 second?

Nope. Distance is velocity x time. The length of the tube of water passing by is d = vt.

 

[SteamKing]

Don't forget to include the time (1 s). It's important to make the units come out right. You should always check that the units come out right!

How are you going to convert that volume of water to a mass value?

According to the OP, the density of seawater is 1030 kg / m³

Would you divide it by the time so 1second? Since the question asks the mass in 1 second?

You're not dividing by time here. The velocity of the flow is 3.5 m/s. The flow rate Q = A × v, and you know A and v.

 

[ultralightbeam]

According to the OP, the density of seawater is 1030 kg / m³You're not dividing by time here. The velocity of the flow is 3.5 m/s. The flow rate Q = A × v, and you know A and v.

Not familiar with that equation:/

 

[SteamKing]

Not familiar with that equation:/

You should be. It's the standard equation of continuity. It's used all the time in pipe flow and such.

The mass flow rate is a modified form: $\dot{m} = ρ A v$

 

[ultralightbeam]

You should be. It's the standard equation of continuity. It's used all the time in pipe flow and such.

The mass flow rate is a modified form: $\dot{m} = ρ A v$

The relevenat equation I know is density = mass /volume

I think writing that out gave me a brainwave..would you multiply the volume by the density, giving an answer of 162.2kg?

 

[SteamKing]

The relevenat equation I know is density = mass /volume

I think writing that out gave me a brainwave..would you multiply the volume by the density, giving an answer of 162.2kg?

The quantity A ⋅ v is the volumetric flow rate, in cubic meters per second.

Multiplying the volumetric flow rate by the density of the fluid in kg / m³ gives the mass flow rate.
This is basic fluid mechanics stuff.

 

[SophiaSimon]

Imagine there is a thin disk of water. The area of this disk is $A=4.5x10^{-2}m^2$. A force is going to be exerted on it, so that it moves in a straight line through the water around it. Because a net force was exerted on the disk of water, it changed its momentum and gained a velocity of $3.5\frac{m}{s}$.

As the disk of water moves, it's going to bump into all the water particles around it. You can find the distance the disk travels using the constant velocity equation. Let's call this distance $l$. You want to find how much mass the disk of water bumped into as it traveled the distance $l$. Let's take the disk to travel through a cylinder whose faces have an area of $A=4.5x10^{-2}m^2$ and whose length is $l$. What is the mass of water in this cylinder that the disk of water bumped into?

You aren't given the mass of water, but the mass density of water, $1030 \frac{kg}{m^{3}}$. This is how much water there is per unit volume. You can find the total mass of water in the volume of the cylinder by using the equation for mass density.