Finding the Second Force and Angle in Cartesian Vector Calculus

In summary, the two forces are 150 N and 200 N, and they act at an angle of 50 degrees. The resultant force is 200 N and is located at (x, y). The angle that force 2 makes with the resultant is determined by the cosine law.
  • #1
spoc21
87
0

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!
 
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  • #2
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 (xr,yr) coordinates of the resultant?

Once you have your diagram, and you've answered the above questions, it should just be algebra.
 
  • #3
ok, so I get the following:


note:V is force 2
VH = x component of vector V (force 2)
VV = y component of vector V

VH = V cos 50
VV = 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)
 
  • #4
Try squaring both sides of the two equations and adding them together.
 
  • #5
hgfalling said:
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!
 
  • #6
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.
 
Last edited:
  • #7
still don't understand how to find the magnitude of the second force..could you please elaborate on this method..

Thanks!
 

What is Cartesian vector calculus?

Cartesian vector calculus is a branch of mathematics that deals with the study of vectors in three-dimensional Cartesian coordinate systems. It involves the use of vector operations such as addition, subtraction, and multiplication to solve problems in physics, engineering, and other scientific fields.

What are the basic operations in Cartesian vector calculus?

The basic operations in Cartesian vector calculus include vector addition, scalar multiplication, dot product, cross product, and vector differentiation and integration. These operations are used to manipulate and analyze vectors in three-dimensional space.

What are some applications of Cartesian vector calculus?

Cartesian vector calculus has numerous applications in science and engineering, including mechanics, electromagnetism, fluid dynamics, and computer graphics. It is also used in the study of motion, force, work, and energy in physics.

What is the difference between a scalar and a vector in Cartesian vector calculus?

A scalar is a quantity that has only magnitude, while a vector has both magnitude and direction. In Cartesian vector calculus, scalars are represented by ordinary numbers, while vectors are represented by an ordered set of numbers (components) and direction angles.

How is Cartesian vector calculus related to other branches of mathematics?

Cartesian vector calculus is closely related to other branches of mathematics such as linear algebra and calculus. It builds upon concepts from these fields to analyze and manipulate vectors in three-dimensional space. It is also used extensively in physics and engineering applications.

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