What is the force exerted by an object on a rope?

[n4rush0]

Homework Statement

Man with mass M pulling with constant horizontal force F along a rope attached to object with mass m. Both the man and the object are on a frictionless surface and separated by distance D. When the man and object meet, what is the velocity of the object? Velocity of the man?

Homework Equations

The Attempt at a Solution

Fnet = ma
Assume motion inwards is positive.
T - F = Ma(subM)
T - F(subobject) = ma(object)

When I draw the free body diagram, what force does the object exert on the rope? How can I "classify" this force? There's no friction, so where would the force of the object come from?

 

[rl.bhat]

Since there is no external force acting on the system, the center of mass remains at rest.
Let r1 be the distance of M from c.m., and r2 be the distance of m from c.m. such that
Mr1 = mr2. And r1 + r2 = D.
Both man and mass experience equal and opposite force F.
The acceleration of man is a1 = F/M, and acceleration of mass is a2 = F/m. They meet at c.m.
Man and mass start from rest. So vi = 0.
Now using kinematic equation find v1 and v2.

 

[n4rush0]

Thanks, I wasn't sure if I could say the force on the man and force on the object both equal F.