Andy (mass 80 kg) uses a 3.0 m long rope to pull Bob (mass 60kg) across the floor (uk= .2) at a constant speed of 1.0 m/s. Bob signals to Andy to stop by plucking the rope, sending a wave pulse forward along the rope. The pulse reashes andy 150 ms later. What is the mass of the rope?

Answer 1

Since Andy weighs more than Bob, and the coefficient of friction is constant, we conclude that Bob moves as Andy pulls.

The normal force on the floor exerted by Bob's weight is N=mg where m=60kg.
the frictional force to overcome is
F=μN

F is also the tension on the rope, T.
The length of the string is L=3m.
The density (mass/length) is m.
The speed of wave propagation is given by
v = L/time
=L/0.15 s
Use
v=√(T/m)
to solve for m.