Finding the Second Force and Angle in Cartesian Vector Calculus

[spoc21]

Homework Statement

Two forces act on an object at an angle of 50°. One force is 150 N. The resultant force is 200 N. Find the second force and the angle that it makes with the resultant, using only cartesian vectors.

Homework Equations

The Attempt at a Solution

Over here, I am very confused. We know that force one = 150 N, so therefore in two space it can be written as [150,0](horizontal on the x axis) in cartesian space. We also know that the resultant force is 200 N, and force 1, and force 2 act at an angle of 50°. I am very confused on how to find the value of force 2, and the angle that it forms with the resultant. Would we use the cosine law? Any help/suggestions to get me started would be appreciated.Thanks!

 

[hgfalling]

You've chosen a coordinate system such that f₁ is [150,0]. You want to find some vector f₂ = (x,y) such that if f₁ and f₂ act at an angle of 50 degrees, the resultant vector is 200 N.

So draw a diagram of the system; your [150,0] vector will lie on the x-axis.
Where will f₂ be?
What is the resultant?
Where will it be?
When they say they want the resultant to be 200 N, what does that mean, in terms of the (x_r,y_r) coordinates of the resultant?

Once you have your diagram, and you've answered the above questions, it should just be algebra.

 

[spoc21]

ok, so I get the following:


note:V is force 2
V_H = x component of vector V (force 2)
V_V = y component of vector V

V_H = V cos 50
V_V = V sin 50

Now we add the two vectors to get the resultant:

150 + V cos 50 = 200 cos (theta)
0 + V sin 50 = 200 sin (theta)


We have two unknowns, theta and V..how could we find the value of either using algebra (very confused) ..Any help is appreciated!

Thanks!

PS (I drew the diagram, and got the above information from it, but had no luck in solving for the unknown values)

 

[hgfalling]

Try squaring both sides of the two equations and adding them together.

 

[spoc21]

Try squaring both sides of the two equations and adding them together.

add them? I'm really confused, how would we find the value of theta, as well as V when both values are unknown, could you please elaborate on your method.

Thanks!

 

[Gigasoft]

Write down an equation for the magnitude of the resultant force in terms of the horizontal and vertical components of the two forces.

Now, find the magnitude of force 2 using this equation. Then, insert it into the equation for the angle.

 

[spoc21]

still don't understand how to find the magnitude of the second force..could you please elaborate on this method..

Thanks!