The portable reel is used to wind up and store an air hose. The tension in the hose is 100 N and a vertical 200-N force is applied to the handle in order to steady the reel frame. Determine the minimum force P which must be applied perpendicular to the handle DE and the vertical components of the force reactions at the feet A, B, and C. The diameter of the coil of reeled hose is 300 mm, and the weight of the loaded reel and its frame may be neglected. Note that force P is perpendicular to OD. State any assumptions.
2. Homework Equations
The scalar force equilibrium equations in three mutually perpendicular directions x-,y- and z-,i.e,
∑Fx=0 ∑Fy=0 and ∑Fz=0
The scalar moment equilibrium equations about three mutually perpendicular axes through a point,i.e,
∑Mx=0 ∑My=0 and ∑Mz=0
The Attempt at a Solution
My assumption initially was that the surface on which the feet of the whole thing rests is frictionless,so that, there are only normal force reactions at A,B and C. Assuming so by balancing the horizontal components of P(which is Pcos 30°) and the 100 N tension(which is 100cos15°) in the hose the value of P obtained doesn't match the given answer(which is given as P=50N).
But If we consider the surface to be rough we will have three mutually perpendicular force reactions at each feet - a normal reaction force and two orthogonal components of the resultant frictional force acting in the plane of the surface.Therefore, we would have to deal with 10 unknowns in the problem including 9 unknown force reaction components at A,B and C and the unknown force P. For the problem to be statically determinate we may allow up to only six unknowns in case of a 3-D force system.What additional assumptions can simplify the problem?