Shaft for a pulley system must be designed to support a 1 ton load. pulley rides

Question

Shaft for a pulley system must be designed to support a 1 ton load. pulley rides on 0.5" diameter ball bearings therefor the shaft must be grooved. pulley leads to a cable spool therefor the shaft is mounted on lubricated sliding bearings enabling it to slide side to side.

-min distance between bearing centers - a=4

I know this is what the shaft will look like, and the dimensions i have shown are previously set. And only static forces are to be analyzed.

How do i analyze that the shaft can support a 1 ton load?

Explanation / Answer

the mass of load is m = 1 ton

the diameter is d = 0.5 inche = 0.5 x 2.75 x 10^-2 m

the weight of the load is w = m x g,g = 9.9 m/s^2

the pressure is

P = (w/A)

where A = pi x (d^2/4)

when the above pressure is greater than the atmospheric pressure,the shaft can support the 1 ton load

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