6.23.
A 12-pack of Omni-Cola (mass 4.30 kg) is initially at rest on a horizontal floor. It is then pushed
in a straight line for 1.20 m by a trained dog that exerts a horizontal force with magnitude 36.0
N. Use the work-energy theorem to find the final speed of the 12-pack if (a) there is no friction
between the 12-pack and the floor, and (b) the coefficient of kinetic friction between the 12pack and the floor is 0.30.
Identify: Apply Wtot  K .
Set Up:
, v2  v . f k  k mg and f k does negative work. The force F  36.0 N is in the
direction of the motion and does positive work.
v1  0
Execute:
(a) If there is no work done by friction, the final kinetic energy is the work done by the
applied force, and solving for the speed,
v
2W
2Fs
2(36.0 N)(1.20 m)


 4.48 m / s.
m
m
(4.30 kg)
(b) The net work is Fs  fk s  (F  k mg )s , so
v
2( F  k mg ) s
2(36.0 N  (0.30)(4.30 kg)(9.80 m / s 2 ))(1.20 m)

 3.61 m/s
m
(4.30 kg)
Evaluate: The total work done is larger in the absence of friction and the final speed is larger
in that case.