Solving Mechanics Basics CW Homework: F and Theta

[Jintachi]

Homework Statement

The question in short: If the resultant force acting on the bracket is 750N along the x positive axis, what is the magnitude of F and the direction (theta)

The Attempt at a Solution

I have tried for several hours now trying to get this done. I have made a table for the components, Fx and Fy.

Fx
325cos(22.61) = 300.0215
600cos(40) = 459.62

Fy
325sin(22.61)=124.9483
-600sin(40) = -385.67

Rx = 759.6415
Ry = -260.6857


But I don't know where to go from there. In all honesty I really don't have much idea on what to do.

Please help me out. Thanks for your time for reading this!

 

[Tanya Sharma]

Is 325N making an angle 22.61 degrees with the horizontal?

 

[Jintachi]

Oops. forgot to mention, I got 22.61degrees from the triangle on the 325N vector.
I got it by doing:
tan-1(5/12) = 22.6198

 

[Tanya Sharma]

Oops. forgot to mention, I got 22.61degrees from the triangle on the 325N vector.
I got it by doing:
tan-1(5/12) = 22.6198

I do not understand . What is 5 and 12 ?

 

[SteamKing]

Oops. forgot to mention, I got 22.61degrees from the triangle on the 325N vector.
I got it by doing:
tan-1(5/12) = 22.6198

You need to review the definition of the tangent.

 

[Jintachi]

I do not understand . What is 5 and 12 ?

You need to review the definition of the tangent.

How would you guys start this? I'm sorry to ask this but I'm fairly clueless. I'm pretty sure what I've said to the above post makes no sense

 

[Tanya Sharma]

You need to write the complete question .It is not clear from the OP what are the given parameters .Please state clearly what is given in the question and if any picture is given in the question then attach the image .

 

[Jintachi]

Can you see the image?

 

[Tanya Sharma]

Okay...

tan^-1(5/12) is the angle which 325N force makes with the vertical not horizontal .

If a force P makes an angle θ with the horizontal then what are its components in x and y directions ?

 

[Jintachi]

Okay...

tan^-1(5/12) is the angle which 325N force makes with the vertical not horizontal .

If a force P makes an angle θ with the horizontal then what are its components in x and y directions ?

Pcosθ for x component, and sin for y?

 

[Tanya Sharma]

Pcosθ for x component, and sin for y?

Yes...horizontal component is Pcosθ and vertical component is Psinθ.

If there are two forces P and R making angles θ and α respectively with the x axis,then the components of the resultant force ,T, in x and y direction (i.e T_x and T_y) will be

T_x = Pcosθ+Rcosα

T_y = Psinθ+Rsinα

i.e we algebraically add the x components to get the x-component of the resultant force .Similarly we do for y-components.

Does this make sense ?

 

[Jintachi]

Yes...horizontal component is Pcosθ and vertical component is Psinθ.

If there are two forces P and R making angles θ and α respectively with the x axis,then the components of the resultant force ,T, in x and y direction (i.e T_x and T_y) will be

T_x = Pcosθ+Rcosα

T_y = Psinθ+Rsinα

i.e we algebraically add the x components to get the x-component of the resultant force .Similarly we do for y-components.

Does this make sense ?

The only part which makes sense is where I have to add the x and y components to get the resultant of x and y. Where do I go from after I have the resultants?

 

[Tanya Sharma]

If the resultant force acting on the bracket is 750N along the x positive axis

This does tell you about the component of the resultant force in x and y direction . What do you infer ?