You need to know the coefficient of static friction between a wooden object and a wooden surface. I'll denote it with <em>µ</em>. If you're given a specific value you should obviously use that.
By Newton's second law, the horizontal and vertical net forces are
• net horizontal:
∑ <em>F</em> = <em>p</em> - <em>f</em> = 0
• net vertical:
∑ <em>F</em> = <em>n</em> - <em>w</em> = 0
where
<em>p</em> = magnitude of the <u>p</u>ushing force
<em>f</em> = mag. of <u>f</u>riction
<em>n</em> = mag. of the <u>n</u>ormal force
<em>w</em> = <u>w</u>eight of the crate
The second equation gives
<em>n</em> = <em>w</em> = (5 kg) (9.8 m/s²) = 49 N
Friction is proportional to the normal force by a factor of <em>µ</em>, so
<em>f</em> = <em>µ</em> (49 N) = 49<em>µ</em> N
To overcome static friction, the push has to exceed this in magnitude, so that
<em>p</em> > 49<em>µ</em> N
For instance, if <em>p</em> = 0.25, then <em>p</em> would need to greater than 12.25 N. (This example isn't particularly helpful, though, since both possibly correct options are larger than 12.25 N...)
