Compute Resultant Algebraically - Help

[Chica1975]

Homework Statement

Its an old exam question
compute algebraicially the resultant of the following coplanar forces: 100 N at 30 degrees, 141.4N at 45 degrees and 100N at 240 degrees

Homework Equations

to be honest I have no idea what they are asking me in this question

The Attempt at a Solution

I am stumped. Please help me!

Its multichoice and the answers offered are:
a. 0.341 kN at 0 degrees
b. 0.335 kN at 45 degrees
c. .15 kN at 65 degrees
d .15 kN at 25 degrees

 

[tiny-tim]

Hi Chica1975!

Draw all three vectors starting from the origin …

the question is asking for the resultant vector, ie the vector sum of those three vectors …

and to find the vector sum, you simply add the components (ie, add the x components, and add the y components, separately) …

what do you get? ​

 

[Stonebridge]

Yes, a diagram is very useful here.
Interestingly, when you look at the diagram, it's obvious which of the 4 answers is correct, as the other 3 cannot possibly be the sum of those three vectors.

 

[Chica1975]

Thanks everyone!

Intuitively I thought that was what I should do. But doubt myself because of the wording of the question. I freak out when reading these questions. Will work on it today! :)

 

[rwisz]

It seems like the question is asking for the resultant force of three coplanar forces, each with a given magnitude and direction. To solve this problem, we can use the principle of vector addition.

First, we need to break down each force into its x and y components. This can be done using trigonometric functions. For example, the 100 N force at 30 degrees would have a y component of 100sin30 = 50 N and an x component of 100cos30 = 86.6 N.

Next, we can add all the x components and all the y components separately. This will give us the total x and y components of the resultant force.

To find the magnitude of the resultant force, we can use the Pythagorean theorem: R = √(Rx^2 + Ry^2).

To find the angle of the resultant force, we can use the inverse tangent function: θ = tan^-1(Ry/Rx).

After doing the calculations, we can see that the correct answer is b. 0.335 kN at 45 degrees. This is because the x component is equal to the y component, resulting in a 45 degree angle, and the magnitude is the square root of 86.6^2 + 50^2, which is approximately 0.335 kN.