Rotating Cylinder Homework: 2kg Mass, 2.5N Force, 1.2m Horizontal Distance

[courteous]

Homework Statement

Cylinder with mass of 2 kg can be rotated around fixed horizontal geometrical axis. Around cylinder's circumference there is wounded rope, end of which is pulled by force equal 2,5 N in a horizontal direction, so that cylinder's rotation is accelerated. In what time does end of the rope move for 1,2 m in horizontal direction?
http://img113.imageshack.us/img113/613/cylinder.png

Homework Equations

• m=2kg
• F=2,5N
• x=1,2m

a_{tangential}=r\alpha
\phi=\omega_0t+\frac{1}{2}\alpha t^2

The Attempt at a Solution

1. First and unsuccessful attempt (solution is 1,0s):
   \frac{F}{m}=a_{tangential}=r\alpha=r\frac{2\phi}{t^2}=r\frac{2\frac{x}{r}}{t^2}=\frac{2x}{t^2}\Rightarrow t=\sqrt\frac{2mx}{F}=1,4s
   
2. While writing this thread, I gave it another shot, this time including inertia I (and getting, what seems, correct solution):
   \frac{2\phi}{t^2}=\alpha=\frac{\tau}{I}=\frac{Fr}{\frac{1}{2}mr^2}=\frac{F}{\frac{1}{2}m\frac{x}{\phi}}=\frac{2F\phi}{mx}\Rightarrow t=\sqrt\frac{mx}{F}=1,0s

What is wrong with first attempt? Ignoring inertia (I) doesn't seem right, but why does (seemingly) rigorous 1. attempt not lead to correct solution (i.e., why is there an extra \sqrt2)?

Yours truly,
courteous.

PS.: Quite likely that I've made grammatical mistakes in 'problem statement'. Please correct me.

 

[LowlyPion]

Solution 2 is correct because it's not F = m*a in 1) is it?

Isn't it really

T = I * α

Where I = 1/2*m*r² and α is rotational acceleration.

 

[tiny-tim]

Homework Statement

Cylinder with mass of 2 kg can be rotated around fixed horizontal geometrical axis. Around cylinder's circumference there is wounded rope, end of which is pulled by force equal 2,5 N in a horizontal direction, so that cylinder's rotation is accelerated. In what time does end of the rope move for 1,2 m in horizontal direction?

PS.: Quite likely that I've made grammatical mistakes in 'problem statement'. Please correct me.

Hi courteous!

Yes, grammar is important!

i] you keep leaving out "a" and "the" (but they're not needed for "with mass")

ii] the present tense is "wind" (rhymes with "mind"), the past tense is "wound" (rhymes with "sound") (but if you stab someone with a sword, the present tense is "wound" (rhymes with "tuned"), and the past tense is "wounded")

iii] "equal to"

iv] never "move for" …

v] why "geometrical"?

A cylinder with mass (or "a mass") of 2 kg can be rotated around a fixed horizontal axis. Around the cylinder's circumference there is wound a rope (or "a rope is wound"), the end of which (or "whose end" or "and its end") is pulled by a force equal to 2,5 N (or "of 2,5 N ") in a horizontal direction (or "horizontally"), so that the cylinder's rotation is accelerated. How long does the end of the rope take to move 1,2 m in the horizontal direction?​

What is wrong with first attempt? Ignoring inertia (I) doesn't seem right, but why does (seemingly) rigorous 1. attempt not lead to correct solution (i.e., why is there an extra \sqrt2)?

Your first attempt is wrong because, in the formula F = ma, a is different for different parts of the cylinder …

if the cylinder was only a cylindrical shell, so that all of it was at distance r from the axis, then I = mr, and your first attempt would be correct …

but for a solid cylinder, a gets less as you get nearer the axis!

 

[courteous]

Solution 2 is correct because it's not F = m*a in 1) is it?

Indeed, I wrongly thought that, for a point where the rope meets the cylinder, Newton's second law would hold.

Isn't it really
T = I * α
Where I = 1/2*m*r² and α is rotational acceleration.

It is. Haven't I correctly used it in 2. attempt?

i] you keep leaving out "a" and "the" (but they're not needed for "with mass")

Cylinder with mass of 2 kg can be rotated around a fixed horizontal geometrical axis. Around the cylinder's circumference there is a wounded rope, end of which is pulled by a force equal to 2,5 N in a horizontal direction, so that the cylinder's rotation is accelerated. In what time does the end of the rope move 1,2 m in a (or the) horizontal direction?​

Any missing or superfluous?

ii] the present tense is "wind" (rhymes with "mind"), the past tense is "wound" (rhymes with "sound") (but if you stab someone with a sword, the present tense is "wound" (rhymes with "tuned"), and the past tense is "wounded")

Haven't thought of second "wound". Nice illustration with sword.

iii] "equal to"

iv] never "move for" …

Very gratious for pointing out my inveterate mistakes.

v] why "geometrical"?

You're right. It really is a tautology, "axis" already harbours "geometrical" ("axis" from latin axis or axle; better yet: sanskrit aksah "an axle, axis, beam of a balance").

tiny-tim, thank you!