Edexcel AS Mechanics 1

Seem to be struggling with this question, could anyone help out?
The centre of mass of a non-uniform beam AB, of weight W and length 4m, is at the point G. The beam rests horizontally on two supports X and Y, where AX = 1m and YB = 2m.
A weight W/4 is suspended from the beam at B. Given that the magnitude of the force exerted on the beam by support Y is three times the magnitude of the force exerted on the beam by support X, calculate the distance AG.

Thanks

Reply 1

Notnek

Original post by Rashina

What have you tried? Post your working.

Reply 2

Keira Larkin

Where did you get this question from?

Reply 3

Reshyna

Original post by Keira Larkin

Where did you get this question from?

Why are you asking?

Reply 4

Keira Larkin

Original post by Rashina

Why are you asking?

Oh I just thought I might be able to find a worked solution if it is from the textbook. :smile:

Reply 5

Reshyna

Original post by notnek

What have you tried? Post your working.

I don't even have an idea of how to do it. Explain me how to do it and I will figure it out.

Reply 6

Reshyna

Original post by Keira Larkin

Oh I just thought I might be able to find a worked solution if it is from the textbook. :smile:

Its from a revision guide which does not have any solution banks or worked solutions.

Reply 7

Keira Larkin

I got these equations so far:

W + W/4 = x + 3x
2W/4 + x = W*z
W(1-z) + 3W/4 = 3x

z is the distance between support y and the centre of mass

Reply 8

Keira Larkin

Original post by Rashina

Its from a revision guide which does not have any solution banks or worked solutions.

Oh okay.

Reply 9

Reshyna

Original post by Keira Larkin

Oh okay.

Anyway thanks for trying to help me

Reply 10

Keira Larkin

Original post by Rashina

Anyway thanks for trying to help me

Well, now I want to know how to solve this as well. There are too many variables in my equations. Have you made any progress?

Reply 11

Reshyna

Original post by Keira Larkin

Well, now I want to know how to solve this as well. There are too many variables in my equations. Have you made any progress?

just calculated the resultant force upwards:
R+3R=(W+W/4)g
Wg= 16x/5

Reply 12

Keira Larkin

Original post by Rashina

just calculated the resultant force upwards:
R+3R=(W+W/4)g
Wg= 16x/5

Is the answer 1.1875m?

WORKING:

So I don't think you multiply W by g because W is weight, which is a force. Therefore, W= 16x/5
Take moments about A to give the equation:
x + (2 * 3x) = Wz + W
7x = W * (z + 1)
7x = 16x/5 (z + 1)
7x * 5/16x = (z + 1)
19/16 = z

(edited 7 years ago)

Reply 13

Reshyna

Original post by Keira Larkin

Is the answer 1.1875m?

Yes! How did you find it?

Reply 14

Keira Larkin

Original post by Rashina

Yes! How did you find it?

Does your textbook say the answer is 1.1875?

Reply 15

Reshyna

Original post by Keira Larkin

Does your textbook say the answer is 1.1875?

The book only has final answers so I found this answer on the book. How did you find it?

Reply 16

Keira Larkin

Basically, the trick was not to take moments about support x or y. I took the moments about point A. Obviously not B because there is a force acting on point B. Refer to the second worked example in the M1 textbook in the section about non uniform planks.

When I do tricky moment questions, I just try taking moments about a point and if that doesn't work, I try another point.