# Homework Help: Help please! cylinder, torque, rolling w/o slipping problem!

1. Dec 17, 2012

### nchin

A massless string is wrapped around a 10 kg cylinder. the picture will look like the letter b. you pull upward on the string with a force of P = 49N. The bottom of the cylinder s on horizontal table and will roll w/o slipping. using dynamics involving center of mass, find the magnitude and the direction of frictional force (f). (no slippage between string and cylinder)

Solution:

Torque about cm: RP - Rf = Iα ---> R(P-f) = Iα

I = 1/2MR^(2)
α = a/R

R(P-f) = 1/2MR^(2) (a/R) ---> P-f = 1/2Ma

Forces Horz: f = ma

Why do we need to consider the forces horizontal?? Isn't it already included in the torque calculation?

P-ma = 1/2Ma
P = 3/2Ma
Ma = 2/3P
a = 2/3 (49N) / 10kg ---> 3.2667 N

My teacher got 32.667N? but how?

2. Dec 17, 2012

### SammyS

Staff Emeritus
You have one equation with two unknowns. You need another equation in the same two unknowns.

f = Ma gives you that.
You solved for a and got 3.2667 m/s2 . (You had the wrong units.)

What does that give you for f ?

3. Dec 18, 2012

### nchin

ooh ok i got it. thanks!