Math Is Fun Forum

Au101

Member

Registered: 2010-12-01

Posts: 353

Centre of mass

Hi again,

I'm very confused about one question, specifically:

Figure 1 shows a uniform triangular lamina ABC placed with edge BC along the line of greatest slope of a plane inclined at an angle θ to the horizontal. The lengths AC and BC are 15cm and 9cm respectively and

is a right angle.

(a) Find the distance of the centre of mass of the lamina from

(i) AB,

(ii) BC.

Now, the centre of mass of a right-angled triangle, unless I am very much mistaken is the point which is one third of the way along each of the sides which form the right angle. Therefore, I would have thought that the answer to (i) is:

cm

and to (ii) is:

cm

However, the whole of part (a) is worth 6 marks. Am I missing something?

Last edited by Au101 (2010-12-15 08:10:04)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Centre of mass

hi AU101,

6 marks does seem a lot for a simple pythagoras and two easy divisions, but I cannot see a way to make this question more difficult to do.  So well done! Have 6 marks!

I'm guessing that there a part (b) in which you have to do something involving theta.

Perhaps the person who made up the question thought "Part b is the bit I really want to test, so I'll give an easy part a just to get them warmed up"

Bob

Last edited by Bob (2010-12-15 23:07:07)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass

Thanks Bob!

Yes it does have a part (b):

Assuming that the plane is rough enough to prevent the lamina from slipping,

(b) find in degrees, correct to 1 decimal place, the maximum value of θ for which the lamina remains in equilibrium.

But even this is only worth 4 marks.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Centre of mass

hi Au101,

That's weird.  I didn't see a diagram so I assumed the lamina was lying flat against the plane.

Having read part B, I'm suspecting this may have been a false assumption.

Any chance of getting a diagram into a post?

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass

Hi Bob, thanks again. Yes the side BC is completely flat against the plane, I have drawn the image in a simple picture editor and have it as a .png file on my computer, but I'm not sure how I would go about uploading it. Part (b) is a style of question which is asking about what happens as you increase the angle of plane. Obviously there will come a point, assuming that the lamina doesn't slide down the plane under gravity, at which the mass acts outside of the lamina, which, obviously, will cause the lamina to roll down the surface. This question is asking for the greatest value of theta for which the lamina remains in equilibrium - i.e. the point at which the mass is acting through the right-angle at the point B. As I'm sure will now be clear to you, all that we need to do is construct a right-angled triangle of base 3 and height 4 (i.e. a right angled triangle from the centre of mass to the plane) and angle theta at the centre of mass. Then, of course, it is a simple tan calculation.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Centre of mass

Hi Au101;

Use image upload. Click for 1 upload. Browse to the file and press submit. Make sure the file obeys the restrictions!

You will probably have an easier time if the file is a .gif rather than a .png

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Centre of mass

Hi Au101,

First I thought the diagram was:

But now I'm thinking:

Anyway, it sounds as though you've got this problem sorted.

I did those pictures in a brilliant software prog. called 'Sketchpad'.  I use it a lot.

Then (and this is a windoze PC) I press PrtSc to snap the screen, paste into 'Paint', edit as required, and then save as a GIF.  The file sizes are pretty small, and I can do what bobbym says and do an image upload.  You cannot do this if you choose a Quick Post.  You have to choose Post Reply for the full range of facilities.

Bob

Last edited by Bob (2010-12-28 02:15:16)

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

Au101

Member

Registered: 2010-12-01

Posts: 353

Re: Centre of mass

Hi,

Thanks, I think I've got it, this is the figure as given in the question.

Thanks .