$3.$ A rope is wrapped over a $6$ cm diameter pipe to support a bucket of tools being lowered. The coefficient of static friction between the rope and the pipe is $0\mathrm{.}20.$

The combined mass of the bucket and tools is $100$ kg$.$

M $=0\mathrm{.}20$

$20$

pipe

r $=3$ cm

bucket

$100$ kg

What is most nearly the range of force that can be applied to the free end of the rope such that the bucket remains stationary?

$560$ N to $1360$ N

$670$ N to $1440$ N

$720$ N to $1360$ N

$720$ N to $1510$ N