Two small blocks, each of mass m are connected by a string of length 4h. Block A

Question

Two small blocks, each of mass m are connected by a string of length 4h.   Block A is placed on a rough tabletop and block B hangs over the edge of the table. There is friction between Block A and the tabletop. The coefficient of friction between block A and table is mu The tabletop is a distance 2h above the floor. Block B is then released from rest at a distance h above the floor and block B begins to accelerate downwards. When block B hits the floor it does not bounce.

The students in the class come up with a list of equations that could be used to describe the motion of Block A: W=Fd, F=muFn, a=Fn/m, Ug + Wnc = Kf, deltaUg=deltaK , deltaK =W     A student predicts the motion of block A once block B hits the floor. "After block B hits the floor, block A will continue to move towards the edge of the table and friction will cause the block to lose energy. The change in KE of block A will be equal to the change in Potential Energy of block B    Block A will have speed =square root of 2gh when block B hits the floor which is enough speed to get it to edge if mu is less than .5"   Which of the above equations support the student's statement and explain how.   Describe how you can determine whether or not block A will reach edge of table.

Explanation / Answer

Here if block B in droperd from the hight h, in h B has potentional energy mgh, if it released that energy is changed into KE due to the movement of B, A also move its initial velocity is zero we can find out the final velosity from the equation v2=u2+2as, here u=0 then v2=2as that is v=sqrt(2as).

then the KE of A is 1/2mv2

ie, KE=1/2 *m*(sqrt(2as))2

ie, KE=1/2m*2as

so KE of A = mas here s=h so mah

so PE of B = KE of A

so that the block A will move towards the edge

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