Given,
The mass of the log, m=50.0 kg
The angle made by the cable with the horizontal, θ=45°
The coefficient of friction, μ=0.450
Friction is a force that opposes the motion of an object. Thus in order to move the log, the tension applied should overcome the friction on the log. That is, the horizontal compound should at least be equal to the friction acting the log.
If you need the log to move at a constant velocity, then the horizontal component of the tension should be equal to the kinetic friction.
Thus,
[tex]\begin{gathered} f=mg\mu \\ =T\cos \theta \end{gathered}[/tex]
Where f is the kinetic friction, g is the acceleration due to gravity, and T is the tension in the string.
On substituting the known values,
[tex]\begin{gathered} 50.0\times9.8\times0.450=T\times\cos 45\degree \\ \Rightarrow T=\frac{50.0\times9.8\times0.450}{\cos 45\degree} \\ =311.83\text{ N} \end{gathered}[/tex]
Thus the necessary tension to drag the log at a constant velocity is 311.83 N
