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Find the Acceleration of the two joined Blocks 
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#1
Feb1513, 05:35 PM

P: 248

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. 


#2
Feb1513, 06:44 PM

HW Helper
Thanks
P: 5,141

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. 


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