hello , i would like you please to find the solution for all of those ,am find it difficult to do them alone i need help!!:eek:

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- Jul 2nd 2007, 01:37 PMcarlasaderforces problem
hello , i would like you please to find the solution for all of those ,am find it difficult to do them alone i need help!!:eek:

- Jul 2nd 2007, 06:50 PMtopsquark
For #1

Recall Newton's 2nd Law:

$\displaystyle \sum F = ma$

and the rotational version of Newton's 2nd Law:

$\displaystyle \sum \tau = I \alpha$

Since the plank is in static equilibrium $\displaystyle \sum F = 0$ and $\displaystyle \tau = 0$

So choose a +y direction to be directly upward. A Free Body Diagram shows that there are four forces present: The forces A and B acting directly upward, the weight w of the woman acting directly downward, and the weight W of the plank also acting directly downward. So we know that

$\displaystyle \sum F_y = A + B - w - W = 0$

$\displaystyle A + B - mg - Mg = 0$

where m and M are the mass of the woman and the plank respectively.

Also choose a positive rotation to be in the counterclockwise sense. I am going to choose an "axis of rotation" to be at the point where the reaction force A is operating. (We may choose*any*point as our axis, since there is no rotation anyway.) We don't know where the CM of the plank is yet, so I'm going to place that at a distance x to the right of the axis of rotation. So

$\displaystyle \sum \tau _A = -(2)w - (x)W + (6)B = 0$<-- That's "2 meters there as the coefficient of w, etc.

$\displaystyle -2mg - xMg + 6B = 0$

We have three unknowns in these two equations.

Well, pick a new axis of rotation and do it again! :) I'll now pick the axis at the point where B is acting, with the same rotation convention. So

$\displaystyle \sum \tau_B = (6 - x)W + (4~m)w - (6~m)A = 0$

$\displaystyle (6 - x)Mg + 4mg - 6A = 0$

This gives us the system of equations:

$\displaystyle A + B - mg - Mg = 0$

$\displaystyle -2mg - xMg + 6B = 0$

$\displaystyle (6 - x)Mg + 4mg - 6A = 0$

We have three equations in three unknowns (A, B, and x), so we may solve this.

I have to get going. If you have a problem solving the system just post in the thread and someone will help you.

-Dan