Solve Acceleration Problem: 10 & 20 lb Blocks, Rope Friction Coefficient 0.2

[eriklee95]

1. A rope connecting a 10 and 20 lb weight passes over a cylinder. The rope-cylinder friction coefficient is 0.2. Rope mass, cylinder radius not given.2. Solve for downward acceleration of the heavy 20 lb block3. I'm confused because this problem doesn't give a mass for the rope, so I assumed we could neglect friction. Then after writing force/tension equations for both masses and combining them, I got 10.7 ft/s^2 as the answer, which isn't one of the options.

 

[gneill]

Even if the rope is massless the masses hanging from it will produce a force on the cylinder. After all, the cylinder is supporting the mass-rope system.

Friction of a rope wrapped around a fixed cylinder is more complicated than the usual frictional force between flat surfaces. Tensions come into play along with the total angle of the "wrap" of the rope. Has this type of frictional setup been presented to you in your course? If not, look up the "Capstan Equation".

 

[haruspex]

Even if the rope is massless the masses hanging from it will produce a force on the cylinder. After all, the cylinder is supporting the mass-rope system.

Friction of a rope wrapped around a fixed cylinder is more complicated than the usual frictional force between flat surfaces. Tensions come into play along with the total angle of the "wrap" of the rope. Has this type of frictional setup been presented to you in your course? If not, look up the "Capstan Equation".

Have you done the calculation? I get a value lower than any of the offered answers.

 

[gneill]

Have you done the calculation? I get a value lower than any of the offered answers.

I have, and I also get a lower value. Looking at the image it seems that the "20 lb" tag may have changed at some point in order to "refresh" the question. Could be the answer choices were not updated. This can be frustrating for students!

 

[haruspex]

it seems that the "20 lb" tag may have changed at some point in order to "refresh" the question.

Well spotted. But I reverse-engineered the mass from the answers and don't get anything encouraging: C)120.8 to 122.4 lb, D) 56 to 56.5 lb, E) 21.2 to 21.3 lb. 120 lb looks hopeful, but it gives 23.5, not 23.6. Other options imply g is being taken as 32.2, which is what I've used.