Question

ENGINEERING MECHANICS: STATICS question:

Determine the resultant force R that is equivalent to the forces exerted
by the three tugboats as they maneuver the barge. Specify the coordinate of the
point on the x-axis through which R passes. (Hint: First determine the resultant
force for the two forces at point A, and then combine this result with the force at
point B.)

Answer 1

I will solve according to your hint:
Solving horizontally: you have to direct all the forces to the horizontal axis and you should add them. At A:
You are given the masses, to get the forces is mg or the masses *10. The masses have to be in kilograms and in 1ton, you have 1000kg.
So: 10*1000*cos35 + 8*1000*cos20=15710N. So to add thaat at B, it does not affect anything to the horizontal adis, because its force is negligible, or its Fcos90=0.
As for the vertical axis at A: 10*1000*sin35 - 8*1000*sin20 = 3000N
NB: this time I subtracted them, because the upward force it above the x-axis, so it is positive, wheres the downward one is below, therefore it is negative.
Using theorem of Pithagoras, the resultant force at A is the square root of sum of the square of those components or R= sqrt( 3000^2 + 15710^2).

Answer 2

I have question. Why is that you didn't use the tugboat of 8 tons going upward?

Answer 3

I just solving the resultant of forces at A only. Including with the b part I do not know how to do it.

Answer 4

Oh i see. I will just add the part B to part A. Thanks for your help. :)

Answer 5

No problem.