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The ambiguity here seems to be the TWO ways of calculating the energy
transferred as (a) the loss of KE of the object, and (b) the work done
by friction.
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A: Suppose that a puck, pushed along a horizontal floor with the
initial kinetic energy K comes to rest. It is stopped by a constant
frictional force, R. The sliding distance, x, should be
x = K / R
B: This can not be exactly correct because part of the initial kinetic
energy is converted into thermal energy (temperature goes up). The
value of x should be less than K/R.
.......................................................................
The puck ... moving with KE across a rough horizontal floor loses
energy to internal forms ... If the frictional force is known, then
the energy so transferred is calculated as the work done by that force.