- #1

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**1. Homework Statement**

Two bars masses m1 and m2 connected by a non deformed light spring at rest on a horizontal plane. The coefficient of friction b/w the blocks and the table is k. What minimum horizontal CONSTANT force F has to be applied on m1 so as to just shift m2.

(For reference Problem 1.123 Irodov).

**2. Homework Equations**

a)F

_{ext}= m*a

_{(cm)}

b)M

_{2}- M

_{1}= W

_{ext}+ W

_{non-conservative}

where M is total mechanical energy.

**3. The Attempt at a Solution**

I got the correct answer by applying the second theorem mentioned above:

Supposing spring constant as a and maximum extension of spring as x and keeping our observations from the time force starts to act upto the time the block m2 first moves.

½a*x

^{2}= F*x + (-km

_{1}gx)

and x = km

_{2}g/a

However I find it hard to digest my own assumption that force will be minimum if the final velocity of m1 is 0. I thought a method involving forces would be easier to understand but it is too complex to work out.Would really appreciate any insight and help that gets me started on a force method.