Question

the coefficient of kinetic friction between a couch and the floor is 0.65. if the couch has a mass of 42 kg and you push it with a force 600 N, what is the net force in the couch as it slides

Answer 1

Explanation:

The net force along the horizontal direction is

$\sum{F_x} = F_{applied} - f$

where f is the frictional force. We can find the frictional force by looking at the vertical forces acting on the couch:

$\sum{F_y} = N - mg = 0 \Rightarrow N = mg$

From the definition of frictional force,

$f = \mu{N} = \mu{mg} = (0.65)(42\:\text{kg})(9.8\:\text{m/s}^2)$

$\:\:\:\:= 267.5\:\text{N}$

Therefore, the net force on the couch is

$\sum{F_x} = 600\:\text{N} - 267.5\:\text{kN} = 332.5\:\text{N}$