A spool has a weight W - 391 lb, outer and inner radii R - 6 ft and p - 4. 3 ft,

Question

A spool has a weight W - 391 lb, outer and inner radii R - 6 ft and p - 4. 3 ft, respectively, radius of gyration k 6- - 3. 9 ft, and mass center at G. The spool is being pulled to the right as shown, and the cable wrapped around the spool is inextensible and of negligible mass. Assume that the static friction coefficient between the spool and the ground i s = 0. 75, and determine the maximum value of the force that the truck could exert on the cable without causing the spool to slip relative to the ground. Before taking any other action, draw a FBD of the spool. The direction of the friction force may not be obvious, as the eccentric tension is tending to impart both translation and rotation in such a way that the acceleration of the spool material point adjacent to the ground is unclear. Consider the following approximate calculation. We can get a sense of the linear and angular accelerations the tension tends to impart from where the "" indicates that these are approximate calculations. Given the clockwise nature of the angular acceleration, the acceleration of the spool material point adjacent to the ground isa - a R. In this problem, we're trying to solve for a threshold tension, so we don't yet know". However, we only need the sign of this approximate calculation to inform the choice of friction force direction in the FBD. Calculate the quantity 1 mrhoR|I0. If this is positive, the motion of the spool material point adjacent to the ground is tending toward the right If negative, ifs tending toward the left. This should enable an informed choice of friction force direction in the FBD.

Explanation / Answer

pool does not slip so at ground the velocity of spool point is 0
so we can say v=R and the spool is spinning clockwise

friction force is towards left

F=ma

T-f=ma

f=mg

T=mg+ma=292.25+12.14a

torque equation:

T+mgR=IG()

R=a

T=7.15a-409.19=292.25+12.14a

a=245.504m/s^2

T=1345.16N

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