- #1

Nova_Chr0n0

- 16

- 3

- Homework Statement
- 2-79. Use the parallelogram law to determine the magnitude of the resultant force acting on the pin. Specify the resultant's direction, measured from the x-axis.

- Relevant Equations
- Cosine Law

Sine Law

Picture above is the complete question. I want to ask about the problem where I would use the parallelogram method. Here is my FBD:

I start off by computing the angle alpha:

α + α + 105 +105 = 360

α = 75 degree

After that, I now use cosine law to solve for the resultant force:

R=[(80)^2+(50)^2-2(80)(50)cos(75)]^(1/2)

R = 82. 640 lb

For the resultant angle with respect to the x-axis, I tried computing for angle beta first:

[sin(β)/80] = [sin(75)/82.640]

β = 69.239

To get theta, I now subtract angles and got:

θ = 90-30-69.239

θ = -9.239 degree

Here where my question starts, my initial thought is that the negative value is acceptable since the angle I'm finding is below the horizontal. But when I did the component method instead of the parallelogram method, I got the position of theta to be wrong.

USING COMPONENT METHOD:

Rx = 80sin(45)+50sin(30) = +81.569 lb

Ry = 80cos(45)-50cos(30)= +13.267 lb

Based on this value, The x component of the resultant force is (+) and the y component is also (+). So the resultant force should be above the x-axis. But in the drawing of my parallelogram, it is below the +x-axis. Is my drawing of the parallelogram inaccurate? or am I missing an important information/knowledge here? If I continue the solution for the component method, I still got 9.239 degree as my answer. But the position the theta in my drawing worries me.