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Granger

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Homework Help Template added by Mentor

## Homework Statement

I have the following problem to solve:

A 1.8m board is placed in a truck with one end resting against a block secured to the floor and the other one leaning against a vertical partition. The angle the Determine the maximum allowable acceleration of die truck if the board is to remain in the position shown.

If you put this problem on google you can find an image (if it helps). The truck moves from left to right.

## The Attempt at a Solution

So I first began to thought that both velocity and acceleration of the board are directed to the right.

The forces acting on the body are its weight, and the normal reactions that the vertical partition and the block exert on the body (which are equal).

Then putting this on equations:

x direction: $$ ma_x=N\cos\theta-N$$

and y direction: $$0=N\sin\theta -mg$$

We have 2 equations and 3 unknowns (N, a and m).

We need a 3rd equation which is

$\frac{d}{dt}L_{system}=\sum(\tau_{net})$

(these are supposed to be vectors)

And so if we choose the bottom block as reference point to gives us angular momentum and torques we have (and this is the equation I'm not sure about)

$$ -m\frac{l}{2}a\sin \theta= lN\sin(105) - \frac{l}{2}mg\sin(165)$$

(the plus and minus sign appear because of the direction of torque and the direction of angular momentum are given by the right hand rule for cross products).

This leading me to a system of 3 equations.

However if I try to solve this system (for example, isolate mass in eq(1) and substitute in eq (2) I end up with N=0 and therefore m=0 which is absurd). Can someone help me figuring out this problem?

Thanks!

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