4) For this question as well, Box A has more mass than Box B. It should be appar

Question

4) For this question as well, Box A has more mass than Box B. It should be apparent tha accelerate downward and Box B will rise. If we cut off a piece of Box B and glue it to Box A, how is the acceleration affected? You must justify your answer using either math or concepts and explicitly state what happens to the acceleration (if anything) t Box A will 5) For this question, use the values that Box A has mass 2M and Box B has mass M. If you release the system from rest, what is the tension in the rope? Give an answer in terms of M and g

Explanation / Answer

4) Here the system considered is a pulley with box A and box B hanging from it on either side.

Let the mass of box B be m1 and that of box A be m2.It is obvious that Box A falls while Box B rises owing to the former's greater weight.

Let a small mass m be cut from box B and attached to box A. Then the new weight of box A is

m2'=m2+m and that of box B is m1'=m1-m.

The equation of motion for the 2 boxes A and B are given below where T is the tension in the string and a is the common acceleration of the 2 masses.

For box B :

T-m1'g=m1'a eq 1)

and for box A:

m2'g-T2=m2'a eq 2).

Solving the above 2 equations we obtain:a=(m2'-m1')g/(m1'+m2').

Substituting the values of m1' and m2' we get a=(m2-m1+2m)/(m1+m2) m/s2. It is obvious that the acceleration of the masses increases on cutting a small mass from box B and gluing it to box A.

5The tension in the string can be obtained by solving the above 2 equations and it turns out to be:

T=2m1m2g/(m1+m2). For m1=M and m2=2M we have T=2*2M*Mg/(M+2M)=4Mg/3 N.

.Note that we are considered the original masses m1 and m2 of the boxes and not m1' and m2'.

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