The end of uniform rope of mass 'M' and length 'L' that is piled on a platform is lifted with a constant velocity 'v' by a variable force F . Find the value of force 'F' as lifted postion of 'x' .

Question

The end of uniform rope of mass 'M' and length 'L' that is piled on a platform is lifted with a constant velocity 'v' by a variable force F . Find the value of force 'F' as lifted postion of  'x' .

anonymous · Answer

Hint:

Start by using this definition of force.  Force is the time rate of change of momentum i.e.$$F=dP/dt=d(mv)/dt=vdm/dt+mdv/dt$$ the mass the force is lifting is changing. the mass at any given instant is 
$$m=\frac{ M }{ L }x$$
where x is the length of rope lifted.  We also know
$$x=vt$$
substitute and solve.