Rope Sag and Force on a Block Being Pulled

[Univarn]

Homework Statement

A block of mass M is pulled along a horizontal frictionless surface by a
rope of mass m, as shown. A horizontal force P is applied to one end of
the rope. (a) Show that the rope must sag, even if only by an imperceptible
amount. Then, assuming that the sag is negligible, find (b) the acceleration
of the rope and block, (c) the force that the rope exerts on the block, and (d) the tension in
the rope at its midpoint.

Homework Equations

sumofF=ma

The Attempt at a Solution

To be honest I don't have a clue on where to start any segment of this problem... Especially part a and part d. Any help you guys can offer would be greatly appreciated. If you need to see the image I'm sure I could upload it somewhere (basically it's just a block M being pulled by a rope m in the right horizontal direction by some force P).

 

[PhanthomJay]

Homework Statement

A block of mass M is pulled along a horizontal frictionless surface by a
rope of mass m, as shown. A horizontal force P is applied to one end of
the rope. (a) Show that the rope must sag, even if only by an imperceptible
amount. Then, assuming that the sag is negligible, find (b) the acceleration
of the rope and block, (c) the force that the rope exerts on the block, and (d) the tension in
the rope at its midpoint.

Homework Equations

sumofF=ma

The Attempt at a Solution

To be honest I don't have a clue on where to start any segment of this problem... Especially part a and part d. Any help you guys can offer would be greatly appreciated. If you need to see the image I'm sure I could upload it somewhere (basically it's just a block M being pulled by a rope m in the right horizontal direction by some force P).

A rope of mass m supported at two points not directly above each other will take the shape of a catenary curve and thus sag (the curved shape approximates a parabola for small sags). This can be shown by equilibrium equations in the vertical direction, where the downward weight must be offset by the vertical upward component of the wire tension (if the wire didn't sag, there would be no upward tension component). The acceleration of the rope and block can be determined from Newton 2 applied to the system; then to find the rope force at certain sections of the rope, take a free body of the rope at at those sections and apply Newton 2 again.

 

[Univarn]

Thanks for your help, I'm still kind of stuck on the rope sag though. Maybe if I could get some help on a free body diagram for the rope with mass? I have going to the right the Fpull, down Fgravity, and up a Fnormal. Not sure where on the free body diagram for the rope I would put Ftension though. Sorry if I'm being a bother, Physics is not my strong point at all.

 

[Doc Al]

Analyze a section of rope in the middle. What forces act on it? If there was no sag, what direction would the tension forces (from the rest of the rope) act? What's the sum of the vertical forces?