The railway crossing gate consists of the 100-kg gate arm having a center of mass at G_a and the 250-kg counterweight having a center of mass at G_W. Determine the magnitude and directional sense of the resultant moment produced by the weights about point A.
Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.
Solution:
Let us write a moment equation around point A. We will assume clockwise movement to be positive.
\circlearrowright M_A=(-100\times 9.81)(2.5+0.25)+(250\times 9.81)(0.5-0.25)
M_A=-2082.5\,\text{N}\cdot\text{m}\circlearrowright
(Notice how we got a negative answer. It simply means the moment being produced is in a counterclockwise direction)
M_A=2082.5\,\text{N}\cdot\text{m}\circlearrowleft\text{(counterclockwise)}
M_A=-2082.5\,\text{N}\cdot\text{m}\circlearrowright
(Notice how we got a negative answer. It simply means the moment being produced is in a counterclockwise direction)
M_A=2082.5\,\text{N}\cdot\text{m}\circlearrowleft\text{(counterclockwise)}
Don’t forget the k in 2082.5 kN*m.
We use kilogram to calculate moments, not grams, so the units used were right. You can write it as 2.0825kN if you like though 🙂