Determine the combined moment about O due to the weight of the mailbox and the cross member AB. The mailbox weighs 3.2 lb and the uniform cross member weighs 10.3 lb. Both weights act at the geometric centers of the respective items. The moment will be positive if counterclockwise, negative if clockwise.

Attached is the complete question but the weight of the mailbox and cross bar differs from the given values which are : weight of mail box = 3.2 Ib, weight of the uniform cross member = 10.3 Ib

Answer : moment of inertia = 186.7 Ib - in

Explanation:

Given data

weight of the mailbox = 3.2 Ib

weight of the uniform cross member = 10.3 Ib

The origin is of mailbox and cross member is 0

The perpendicular distance from Y axis of centroid of the mailbox

= 4 + (25/2) = 16.5"

The centroid of the bar =( ( 1 + 25 + 4 + 4 ) / 2 ) - 4 = 13"

therefore The moment of Inertia( Mo) = (3.2 * 16.5) + ( 10.3 * 13)

= 52.8 + 133.9 = 186.7 Ib-in

AFOKE88 AFOKE88 · Answer 2 · 2021-11-28T12:15:58+01:00

The combined moment about O due to the weight of the mailbox and the cross member AB is; M_o = 122.4 lb.in (ccw)

We are given;

Weight of mailbox; W_m = 3.2 lb

Weight of uniform cross member; W_c = 10.3 lb

Now, from the attached diagram, let us calculate the geometric location of the mailbox and uniform cross section from point O.

Geometric location of mailbox from point O; g_m = 3 + (19/2) = 12.5 in

Geometric location of cross member from point O;

g_c = (¹/₂(1 + 19 + 3 + 7)) - 7

g_c = 8 in

Thus. combined moment about point O is;

M_o = (W_m × g_m) + (W_c × g_c)

M_o = (3.2 × 12.5) + (10.3 × 8)

M_o = 122.4 lb.in

Since positive then it is counterclockwise. Thus;

M_o = 122.4 lb.in (ccw)

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