Answer:
[tex]\mu > 0.225[/tex]
Explanation:
The cable snapped because the frictional force [tex]f_s[/tex] was greater than the tension in the rope:
[tex]f_s > 4,500N[/tex]
Now,
[tex]f_s =\mu N[/tex]
where [tex]\mu[/tex] is the coefficient of static friction, and [tex]N[/tex] is the normal force. In our case, the normal force on the compressor is 20,000 N; therefore,
[tex]f_s =\mu (20,000N )[/tex].
Putting this into the condition [tex]f_s > 4,500N[/tex], we get:
[tex]\mu (20,000N )> 4,500N[/tex]
[tex]$\mu > \frac{4,500N}{20,000N} $[/tex]
[tex]\boxed{\mu > 0.225.}[/tex]
