Question

A spring is compressed between two toy carts of mass m1 and m2. When toy carts are released, spring exerts equal and opposite forces on each toy cart for equal time interval 't'. If coefficient of friction between ground and cart is 'u' then find ratio of displacement of both carts

Answer 1

let the displacements be s1 and s2 coefficient of friction=U
frictional force=UR=Umg
or,ma=Umg
or,a=Ug
v^2=u^2+2as (u=o)
v=sqrt(2as)
now since they exert equal but opposite force so
F1 = - F2
or,change in momentum of m1= - change in momentum of m2
or m1*v1= -m2*v2 (time cancels)
or m1*sqrt(2as1) = - m2*sqrt(2as2)
squaring,
m1^2 * 2as1 = - m2^2 2as2
so s1/s2=-(m2^2.m1^2)