Answer:
226.6 N
Explanation:
The work done by the push is given by:
[tex]W_p = p d cos \theta[/tex]
where
p is the magnitude of the push
d is the displacement of the crate
[tex]\theta=30^{\circ}[/tex] is the angle between the direction of the push and the displacement of the crate
On the contrary, the work done by the frictional force is:
[tex]W_f = - F_f d[/tex]
where
[tex]F_f = \mu mg[/tex] is the frictional force, with m=1.00x102 kg being the mass of the crate ang g=9.81 m/s^2 the gravitational acceleration
d is the displacement of the crate
the negative sign is due to the fact that the frictional force acts in the opposite direction to the displacement of the crate.
The net work must be zero, so:
[tex]W_p + W_f =0[/tex]
Substituting the previous equations into this one, we find:
[tex]pd cos \theta - \mu d mg=0[/tex]
which we can solve to find p:
[tex]p=\frac{\mu mg}{cos \theta}=\frac{(0.200)(1.00\cdot 10^2 kg)(9.81 m/s^2)}{cos 30^{\circ}}=226.6 N[/tex]