Question

Cionsider the situation of the previous problem. Suppose each of tbe blocks is pulled by a constant foerce F instead of any impulse. Find the maximum elongation that the spring will suffer and the distancews moved by the two blocks in the process.

Answer 1

Correct Answer - A::B
If both blocks are pulled by some force they suddenly move with some acceleration and instntaneously stop at same positioin where the elongation of sprin is maximum.
`rarr x_1,x_2rarr` extansion by block `m-1 and m_2`
Total work doen `=Fx_1+Fx_2`......i
`:.` Inccreases the potential energy of spring
`=1(1/2)K(x_1+x_2)^2`..........2
Equating 1 and 2
`F(x_1+x_2)(1/2)K(x_1+x_2_)^2`
`F(x_1+x_2)=(1/2)K(x_+x_2)^2` ltbr. `rarr (x_1+x_2)=((2F)/k)`
Since the net exterN/Al force on the two blocks is zero ths same force acts on oppostie directions
`:. m_1x_1=m_2x_2` .......3
and `x_1+x_2=(2F)/k`
`:. x_2=m_1/m_2 x_1`
`Substituing m_1/m_2x_1+x_1=(2F)/k`
`rarr x_1(1+m_1/m_2)=(2F)/k`
`x_1=(2Fm_2)/(k(m_1+m_2))`
`x_2=(2Fm_1)/(k(m_1+m_2)`