Required tangential force to move spool

[Dan Aiken]

This should be an easy one, but my answer does not seem right to me. I was hoping someone to verify for me.

If you have a spool filled with rope that weighs 2,000 LBS on a frictionless axle. Determine the tangential force required to move the spool by pulling the rope.

Given:
Weight of spool = 907.18 KG
Diameter of spool = 1.22 Meters
Angular Acceleration = 2.093 RADs per Second
Length of spool = .74 Meters
T = Torque
A = Angular Acceleration
R = Radius of spool in meters

Explanation of calculations:

I calculated the moment of inertia for the full spool and used it to derive the torque (knowing the angular acceleration) and then derived force out of the torque equation.

Calculations:

I = 1/2*M*(L squared)
I = .5*907.18*.547
I = 248.11 KG*(Meters squared) Moment of inertia in Kg*Meters - squared

If I = T/A then

248.11*2.093 = T
T = 519.29 Newtons*Meters

If T = F*R then519.29 / .61 = F
F = 851.29 Newtons

As far as my tension in rope I assume it to be equal to F at 851.29 Newtons Is this correct? The value seems high to me. Please advise.

 

[CWatters]

I haven't checked your working but...

851 Newtons is about the same force that an 85kg man exerts on the ground due to gravity. That doesn't seem like a lot given your 2000lb spool accelerates at 2 rad/s/s. (about 114 deg/s/s)