As level mechanics unit 1 question on moments.

[Pagey]

Homework Statement

A non-uniform plank of wood AB has length 6m and mass 90kg. The plank is smoothly supported at its two ends A and B, with A and B at the same horizontal level. A woman of mass 60kg stands on the plank at the point C, where AC=2m. The plank is in equilibrium and the magnitudes of the reactions at A and B are equal. the plank is modeled as a non-uniform rod and the woman as a particle. Find

(a) the magnitude of the reaction on the blank at B,

(b) the distance of the centre of mass of the plank from A.

Homework Equations

- general knowledge on moments.

The Attempt at a Solution

(a) i was going to take moments about the point A, therefore as the reaction force (R) at A acts through A its moment will = 0, therefore allowing me to find the reaction force (R) at B knowing the moment of the woman at A is (60g* x 2) *where g=9.8, but as the rod is non uniform i can't assume the rods mass (90kg) acts at the centre, i.e. 3m away from A (therfore the moment at A can't be 90g x 3), therefore i don't know how to take this into account without creating a distance X for the mass from A, which would only lead me onto part B anyway.

?

Thanks Mike.

 

[Doc Al]

Hint: What must the total reaction force from both supports equal?

 

[Pagey]

The total reaction force must equal the total downard force, i.e. 60g +90g for the woman and plank, even so i don't see how this can help me with the problem of not knowing the distance of the 90g when taking moments at A?

 

[Pagey]

O wait it can't be as simple as that the total reaction force must equal the total downard force, so as A and B are the same its just 90g+60g?

 

[Doc Al]

Yes, it's that simple.