  Picking up, laying down, colliding, rolling, and peeling are partial-contact
interactions involving moving discontinuities. We examine the balances of
momentum and energy across a moving discontinuity in a string, with allowance
for injection or dissipation by singular supplies. We split the energy
dissipation according to its invariance properties, discuss analogies with
systems of particles and connections with the literature on shocks and phase
transition fronts in various bodies, and derive a compatibility relation
between supplies of momentum and translation-invariant energy. For a moving
contact discontinuity between a string and a smooth rigid plane in the presence
of gravity, we find a surprising asymmetry between the processes of picking up
and laying down, such that steady-state kinks in geometry and associated jumps
in tension are not admissible during pick-up. This prediction is consistent
with experimental observations. We briefly discuss related problems including
the falling folded chain, peeling of an adhesive tape, and the "chain
fountain". Our approach is applicable to the study of impact and locomotion,
and to systems such as moored floating structures and some musical instruments
that feature vibrating string and cable elements interacting with a surface.
