Answer to Question #259818 in Mechanical Engineering for Jool

Question

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.

Answer 1

Solution;

Given;

Mass,m=10lb

Local gravity,g=31.1ft/s²

Vertical force ,F=8lbf=257ft.lb/s²

We know;

$W=mg=10×31.1=311\frac{ft.lb}{s^2}$

(a)

Downward;

The total force ,F_T;

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

But ;

$F=m×a_d$

The acceleration of the mass is;

$a_d=\frac Fm=\frac{568.4}{10}=56.84ft/s^2$

(b)

Upward;

$F_T=W-F=311-257.4=53.6\frac{lb.ft}{s^2}$

Hence;

$a_u=\frac FM=\frac{53.6}{10}=5.36ft/s^2$