Find the Acceleration of the two joined Blocks

Northbysouth

1. The problem statement, all variables and given/known data
The sliders A and B are connected by a light rigid bar of length l = 0.50 m and move with negligible friction in the slots, both of which lie in a horizontal plane. For the position where x_A = 0.4 m, the velocity of A is v_A = 0.80 m/s to the right. Determine the acceleration of each slider and the force in the bar at this instant. The acceleration of A is positive if to the right. The acceleration of B is positive if up (if that is the right word in this horizontal plane). The force in the rod is positive if in tension. Remember that the motion takes place in a horizontal plane, so the force of gravity is not a factor.


2. Relevant equations



3. The attempt at a solution

I drew FBD of blocks A and B.

Block A has force P acting on it to the right, and there is a force F pointing along the direction of the attached rod.

ƩR_x = ma_A = P - Fcos(phi)

Then I drew a FBD of block B which has the force F acting on it as well in the direction of the rod. Aside from this I can't see any other forces acting on block B.

ƩF_z = ma_A = -Fcos(θ)

After this I'm stuck. I think I need another relationship, one relating the acceleration of block A and B. I'm thinking the Pythagoras theorem would work, but I'm not sure, how I should adapt it for this situation.

Any input would be appreciated.

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NascentOxygen

For the triangle, x² + y² = 0.5²

If you differentiate this twice w.r.t. time, you'll have the acceleration of x ❲viz., ^d²x/_dt²❳ related to the acceleration of y ❲viz., ^d²y/_dt²❳

Does this sound like the method you expect? I don't want to mislead you, I don't know whether calculus is essential to solving this.