Centres of mass integration

See question below,

For part b of this question do i have to go through the integration algebraically like in part a, or is it enough to set up the integral and then find the value on my calculator, given it's pretty obvious before doing it that the exact value isn't going to be very useful.

(edited 1 year ago)

my workings for it, the integration isn't bad, it's just time consuming and it would save 2-3 min if I could just plug it into my calculator

Reply 3

mqb2766

Can you upload the question pic again, its almost unreadable.

Id guess for 6 marks theyd want you to calculate xbar, as getting ybar in part a) is 4 marks.
Its a fairly simple ibp so that would probably hint that they want the proper solution.

Reply 6

Skiwi

Original post by mqb2766

Id guess for 6 marks theyd want you to calculate xbar, as getting ybar in part a) is 4 marks.
Its a fairly simple ibp so that would probably hint that they want the proper solution.

ok, just wanted to check just in case. Can i just state what the square brackets equal to, or would i better off just going through the algebra and giving the exact solution and then to 3dp?

On a sidenote, i think it's a bit weird how the marks are awarded for this question. Finding xbar is more work than ybar, yet they give more marks for finding ybar.

Reply 7

mqb2766

Original post by Skiwi

You get 4 marks for ybar (and the answer is given to check your approach) and 6 marks for xbar & angle. So that sounds about right to me?

Id guess evaluating the square brackets would be ok (note the guess). You could simplify the logs in the expression a bit to get
ln(2^(1/2) / 5^(1/5))
but its still going to be a 3 sig fig answer, not an exact expression.

Reply 8

Skiwi

Original post by mqb2766

Given that it's not a definite yes i think i'll play it safe and put it all down.

The mark scheme allocates 3 marks for xbar and 3 for the angle, but thinking about it a bit more i think it's down to the fact you have to work out the area of region in part a, so finding xbar in part b is reduced to just evaluating 1 integral instead of 2.

Reply 9

mqb2766

Original post by Skiwi

Quite possibly, Ive not seen the mark scheme. When they give you the answer to check, like in part a), it can be to get the approach sorted. Then "repeating" it in b) (with a bit variation) gets ~same marks, but cant say for definite why there is 1 mark difference. If its 3 marks, Id guess evaulating the square brackets would be sufficient, but sometimes its hard to say exactly what marks are allocated for.

Reply 10

Skiwi

Original post by mqb2766

Another centres of mass question that i didn't think warranted a new thread is what you would interpret -Centre of mass (discrete mass distribution)- as, it's bullet pointed in the advanced information so there will be a question on it but i can't find it in my textbook, unless it's it's just being called something else.

Reply 11

mqb2766

Original post by Skiwi

Id guess theyre talking about calculating the com by summing over a small number of "elementary" objects where each of the elementary com is known/easy to calc. So contrast this with a continuous integration approach (this thread) to calculate the com of a single object.