The net force on the mass in the vertical direction is
∑ <em>F</em> = <em>n</em> - <em>w</em> = 0
and the net horizontal force is
∑ <em>F</em> = <em>A</em> - <em>f</em> = <em>ma</em>
where
<em>n</em> = magnitude of the normal force
<em>w</em> = <em>mg</em> = weight of the mass
<em>m</em> = 10 kg, mass of the … uh, mass
<em>g</em> = 9.8 m/s², mag. of acceleration due to gravity
<em>A</em> = 69 N, mag. of the applied force
<em>f</em> = mag. of kinetic friction
From the first equation, we get
<em>n</em> = <em>mg</em> = (10 kg) (9.8 m/s²) = 98 N
Then the friction force has magnitude
<em>f</em> = <em>µ</em> <em>n</em> = 0.5 (98 N) = 49 N
Solve the mass's acceleration in the second equation:
69 N - 49 N = (10 kg) <em>a</em>
<em>a</em> = (20 N) / (10 kg) = 2.0 m/s²
in the positive <em>x</em> direction.
