# Physics n00b

1. Feb 3, 2005

### ][nstigator

I know nothing bout this stuff, lil help? :P

I have no idea what this means

What are the dimensions of viscosity η if the equation for the force on a sphere moving through liquid is F=6πηrv where r is the radius of the sphere, v is the speed and F is the force?

or this...

Show that the equation for the final velocity of an object undergoing uniform acceleration is dimensionally consistent.
v² = u²+2as

could someone help me out and explain what I need to do for these questions

2. Feb 3, 2005

### arildno

Do you know what "dimension" means in this context?

3. Feb 3, 2005

no I dont :(

4. Feb 3, 2005

### arildno

If I ask you what "units" does force have, does that help?

In this context, "dimension" means "units"

5. Feb 3, 2005

### ][nstigator

force is newtons or something right?

6. Feb 3, 2005

### arildno

Absolutely right!

In this case, try to write "newtons" in terms of the base type of units "kilograms" "meter" "second"

Also set up what units velocity has in these base units.

7. Feb 3, 2005

### ][nstigator

velocity is metres/second/second isnt it? ms^-2 ???

8. Feb 3, 2005

### arildno

Nope, that's acceleration".

Velocity measures how far (a length!) you travel over a period (that's a time!).

So, the units of "v" is $$[v]=\frac{m}{s}$$
Now, the units of force is newtons, which also can be written as:
$$[F]=N=kg*\frac{m}{s^{2}}$$ (mass times acceleration!)
(I use the bracket notation, say [F], to mean I'm interested in the UNITS of F, not its particular measured value. Okay?)

$$F=6\pi\eta{rv}$$
You need to end up with the same type of units on both sides of the equation, so you must have:
$$[F]=[\eta][r][v]$$ ($$6\pi$$ is just a number without dimebsion)
Now, let's fill in:
$$kg*\frac{m}{s^{2}}=[\eta]\frac{m^{2}}{s}$$

What units is therefore $$[\eta]$$ ?

9. Feb 3, 2005

### ][nstigator

η= kg (ms)/(s^2*m^2)

is that right?

10. Feb 3, 2005

### arildno

Yep!
But try simplifying that expression a bit!

11. Feb 3, 2005

### arildno

Oops!
Just to make it absolutely clear, what you've found, are the DIMENSIONS of $$\eta$$
that is $$[\eta]$$, not $$\eta$$ itself..

12. Feb 3, 2005

### ][nstigator

but thats what I needed to find in the question anyways :P

η= kg*1/ms? is that the simplified one?

what about that other question, how do I do that?

13. Feb 3, 2005

### arildno

You've got the simplified one correct: $$[\eta]=\frac{kg}{ms}$$
You have only been asked to find the UNITS, not the numerical value of the viscosity.
(That's just the same as saying that all lengths can be measured in "meters", but that doesn't mean the lengths can't have different values (say, one length is 2meters, another 3meters)

Each term in your equation must have the same dimensions.
You have three "terms:
$$v^{2},u^{2},2as$$
I'll leave it to yourself to verify that these three terms have, indeed, the same dimensions.

14. Feb 3, 2005

### ][nstigator

so that answer for the 1st would be correct considerin what the question is asking?

Im still not sure what I need to do for that second one

v^2 = final velocity
v^2 = (m/s)^2

u^2 = initial velocity
u^2 = (m/s)^2 also

2as = 2*acceleration*distance
2as = 2((m/s^2)*m) = 2(m^2/s^2)

umm, am I way off? or kinda on the right track?

15. Feb 3, 2005

### ][nstigator

oh wait

its just the terms right
so

as=(m^2/s^2) = (m/s)^2

16. Feb 3, 2005

### Integral

Staff Emeritus
Looks like you have it figured out. Good job.

17. Feb 3, 2005

### ][nstigator

yay! thankyou
I got a few other questions, I think I know them, but I dont want to learn how to do something wrong :P

What are the dimensions of
a)momentum (mass x velocity)
b) work (force x displacement)
c) impulse (force x time)

a) p=mv
b) J=Fm
c) I=Ft

is that right?

18. Feb 3, 2005

### jdstokes

I'd set out the first problem like this
\begin{align*} \left[v^2\right] &= \rm m^2\, s^{-2} \\ \left[u^2\right] & = \rm m^2\, s^{-2} \\ \left[2as\right] & = \left(\rm m\, s^{-2}\right)(\mathrm{m}) \\ & = \rm m^2\, s^{-2} \\ \intertext{therefore} \left[u^2 + 2as\right] & = \rm m^2\, s^{-2} \\ & = \left[v^2\right] \end{align*}

The units of momentum are $[p] = \mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-1}$,the units of work are $[W] = \mathrm{N}\,\mathrm{m} = (\mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-2})(\mathrm{m})=\mathrm{kg}\,\mathrm{m}^{2}\,\mathrm{s}^{-2}$, and the units of impulse are $[J] = (\mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-2})(\mathrm{s}) = \mathrm{kg}\,\mathrm{m}\,\mathrm{s}^{-1} = [p]$.