Physics

**LittleGrizzly** · 05-19-2008, 17:03

Seems like the best place to put this,
I have a test coming up on circular motion and i would like one of you guys to check over my answers as i missed a few of the lessons we had on it so the teacher gave me a quick half hour run through of it, i think i mostly get it but i want to make sure im not messing anything easy up.
1. The planet venus can be assumed to orbit the sun in a circular orbit whose radius is 1.08 x 10 (11) m (in brackets is to the power of). The mass of the sun is 2.00 x 10 (30) kg
write down an expression for
(i) the gravitational force on venus
(ii) the centripetal force required to act on venus to enable it to travel in a circularorbit. Use the fact these two expressions represent the same force to calculate the angular velocity of venus in its orbit.
Use the angular velocity to determine
a) the linear velocity of venus and
b) the period of the orbit of venus.
express your answer to b) in days
and heres my answers...

1i) F = G (m1 x m2 / r (2) )
Force = Gravitation constant x mass of object 1 x mass of object 2 / distance between object centres

ii) F= m2 r w (2)
Force = mass of object 2 x radius x angular velocity (2)

m2 x r x w (2) = G x m1 x m2 / r (2)
m2 (mass of venus) cancels leaving

r x w (2) = G x m1 / r (2)
(1.08 x 10 (11) ) x w (2) = (6.67 x 10 (-11) ) x (2.00 x 10 (30) ) / (1.08 x 10 (11) )
(1.08 x 10 (11) ) x w (2) = 0.01143689986

w (2) = 1.05897221 x 10 (-13)
w = 3.25418532 x 10 (-7)

a) v = r x w
v = 1.08 x 10 (11) x 3.25418532 x 10 (-7)
v = 35145.20146 ms - 1

b) T = 2pi/w
Time = 2 x pi (3.14) / angular velocity

Time = 19298224.85 seconds
321637.0808 minutes
5360.918013 hours
223.3590839 days orbit for venus around the sun

**Ferret** · 05-19-2008, 19:26

I'm afraid the question is a little too complicated for me but for future reference '^' without the quotation marks stands for 'to the power of'. Sorry I can't help you with that though...

**PBI** · 05-19-2008, 20:52

Is this assessed work? If so asking about it on the internet is probably cheating and we shouldn't help you.

If it's a practice question or a past paper that's OK.

Without going into specifics though it looks to me like you've got the general idea right

.

**LittleGrizzly** · 05-19-2008, 22:57

lol no don't worry its a past question, its more about the method than the figures, and using the right formula for the right question.

thanks ^ would make it a lot less confusing with all the brackets

**PBI** · 05-19-2008, 23:22

In that case, yes, your formulae appear to be correct to me.

I assume you know the best method for checking whether you've done a question right, i.e. do you get a sensible answer? In this case your answer is a Venusian year of about 2/3 of an Earth year, which sounds sensible. If you'd got a value of 20 seconds, that's a sign you need to start looking for your mistake. Sounds obvious but you'd be amazed how many lab books I mark with people happily concluding that the Earth weighs about a gram or has a radius of several light years.

Good luck with your test.

PS You really don't need to quote numbers to that many decimal places. A good rule of thumb is about 2 or 3 dp or sf, whichever seems more sensible.

**LittleGrizzly** · 05-20-2008, 01:47

I assume you know the best method for checking whether you've done a question right, i.e. do you get a sensible answer? In this case your answer is a Venusian year of about 2/3 of an Earth year, which sounds sensible. If you'd got a value of 20 seconds, that's a sign you need to start looking for your mistake. Sounds obvious but you'd be amazed how many lab books I mark with people happily concluding that the Earth weighs about a gram or has a radius of several light years.

I usually think about how logical the answer is, that has messed me up once or twice when i didn't believe the answer i had produced and checked and rechecked until the teacher told me i was right in the first place.

I go for 3 dp's usually i just wanted to keep the numbers as close as possible as i was expecting mistakes... Thanks

**TevashSzat** · 05-20-2008, 02:52

Did a quick look there and everything seems alright.

**Marcellus** · 05-20-2008, 03:46

The working's all fine. You're given data to three significant figures so a good rule of thumb would be to give your answers to a similar precision.

**Ironside** · 05-20-2008, 07:48

You can check the orbital period for Venus on the net, 224.70069 days. With rounding errors, does this look reasonable?

And the formulas look correct by me, although personally I would use different formulas, but that's purely by taste.

**Viking** · 05-20-2008, 09:29

And compare the orbital period with the rotation period and you'll be up for a surprise.

**LittleGrizzly** · 05-20-2008, 09:33

Im only a day off so im guessing its ok, if i had got the formulae wrong it would probably be a fair bit off.

These are the formulas the teacher gave me so i probably have to use them ;)

ok thanks for all the help guys (your like a more accessible teacher with unlimited knowledge, or at least it seems that way) test in a few hours, wish me luck!

Edit: the orbital period is close to the rotation period ?

**Viking** · 05-20-2008, 09:53

Originally Posted by LittleGrizzly

Edit: the orbital period is close to the rotation period ?

The rotation period is, in fact, longer.

**LittleGrizzly** · 05-20-2008, 12:00

Test went well, pretty much full marks apart from me saying the centripetal force acting on the earth is due to the gravity of the sun, i got the marks but he wasn't really happy with that answer. So thanks again!