Question #259818

A 7 lbm piece of steel is subjected to a vertical force of 8 lbf. The local gravity is 31.1 ft/s2, and frictional effects are neglected. Determine the acceleration of the mass if the external vertical force is (a) downward, (b) upward in ft/s2.

1
Expert's answer
2021-11-05T03:39:40-0400

Solution;

Given;

Mass,m=10lb

Local gravity,g=31.1ft/s2

Vertical force ,F=8lbf=257ft.lb/s2

We know;

W=mg=10×31.1=311ft.lbs2W=mg=10×31.1=311\frac{ft.lb}{s^2}

(a)

Downward;

The total force ,FT;

FT=W+F=311+257.4=568ft.lbs2F_T=W+F=311+257.4=568\frac{ft.lb}{s^2}

But ;

F=m×adF=m×a_d

The acceleration of the mass is;

ad=Fm=568.410=56.84ft/s2a_d=\frac Fm=\frac{568.4}{10}=56.84ft/s^2

(b)

Upward;

FT=WF=311257.4=53.6lb.fts2F_T=W-F=311-257.4=53.6\frac{lb.ft}{s^2}

Hence;

au=FM=53.610=5.36ft/s2a_u=\frac FM=\frac{53.6}{10}=5.36ft/s^2





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