Question

A large spool of rope stand on the ground with the end of the top edge of the spool. A person grabs the ends of the rope and walks a distance $l$, holding onto it figure. The spool rolls behind the person without slipping. What is the length of rope that unwinds from the spool? How far does the spool's $CM$ move?

• A. Length of rope that unwinds from the spool is $l$
• B. Length of rope that unwinds from the spool $\frac{l}{2}$
• C. Spool's CM moves through $\frac{l}{2}$
• D. Spool's CM moves through $l$

Answer 1

Answer: (B), (C)

Spool's CM moves through $\frac{l}{2}$
Length of rope that unwinds from the spool $\frac{l}{2}$

$V_{\text{top relative to the ground}}=V_{\text{top relative to the center}}+V_{\text{center relative to ground}}=v+v=2v$

The length of wire that unwinds from the rope is $\frac{l}{2}$

Therefore if the person moves a distance $l$ the the spool's CM moves through a distance $\frac{l}{2}$