Setting up Forces: Finding Theta of F2

In summary, the conversation is about setting up a problem involving three forces acting on a bracket and determining the magnitude and direction of F2 to achieve a resultant force along the positive u axis with a magnitude of 50lb. The individual is having trouble evaluating the tan(25+theta) part and is seeking help. They are advised to use the angle sum identity for tangent or solve for tan(25° + θ) and subtract 25° for a numerical result.
  • #1
whynot314
76
0
I am curious if I am setting this problem up right.

Three forces act on the bracket. Determine the magnitdue and direction theta of F2 so that the resultant force is directed along the positive u axis and has a magnitude of 50lb.

[URL=http://s1341.photobucket.com/user/nebula-314/media/20130520_221430_zps840432f0.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130520_221430_zps840432f0.jpg[/URL][/PLAIN]


[URL=http://s1341.photobucket.com/user/nebula-314/media/20130520_222748_zps3f68f545.jpg.html][PLAIN]http://i1341.photobucket.com/albums/o745/nebula-314/20130520_222748_zps3f68f545.jpg[/URL][/PLAIN]

This is how i set it up. If this set up is correct I am having trouble evluating the tan(25+theta) part. If there is an easier way please help.
 
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  • #2
sorry for the verticle photo.
 
  • #3
whynot314 said:
I am curious if I am setting this problem up right.

Three forces act on the bracket. Determine the magnitdue and direction theta of F2 so that the resultant force is directed along the positive u axis and has a magnitude of 50lb.

[ IMG][ URL=http://s1341.photobucket.com/user/nebula-314/media/20130520_221430_zps840432f0.jpg.html][ [Broken] IMG]http://i1341.photobucket.com/albums/o745/nebula-314/20130520_221430_zps840432f0.jpg[/URL] [Broken]


[ IMG][ URL=http://s1341.photobucket.com/user/nebula-314/media/20130520_222748_zps3f68f545.jpg.html][ [Broken] IMG]http://i1341.photobucket.com/albums/o745/nebula-314/20130520_222748_zps3f68f545.jpg[/URL] [Broken]

This is how i set it up. If this set up is correct I am having trouble evluating the tan(25+theta) part. If there is an easier way please help.
You could use the angle sum identity for tangent: ##\displaystyle \ \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}\ .##

But I think it would be better to solve for tan(25° + θ), then take the arctan of both sides to get a numerical result for 25° + θ . (Make sure that's in degrees.) Subtract 25° from that.
 
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  • #4
ahhhhh ok thanks, ill try this in the morning.
 
  • #5


I would first commend the individual for setting up the problem with clear diagrams and equations. However, I would suggest a few adjustments to make the problem easier to solve and evaluate.

Firstly, instead of using the angle theta, I would suggest using the angle between F2 and the positive u axis, which we can call alpha. This will make it easier to evaluate the trigonometric functions.

Next, I would suggest using the component method to solve for the resultant force. This involves breaking down each force into its x and y components and then adding them together to get the resultant force. This method will allow for easier evaluation of the trigonometric functions without having to use the angle theta.

To set up the equations for the component method, we can use the following equations:

F1x = F1 * cos(25)
F1y = F1 * sin(25)
F2x = F2 * cos(alpha)
F2y = F2 * sin(alpha)
F3x = F3 * cos(90)
F3y = F3 * sin(90)

Next, we can set up the equation for the resultant force in the x direction:

Rx = F1x + F2x + F3x

Since we want the resultant force to be directed along the positive u axis, we can set Rx equal to 50lb. This will give us the following equation:

50 = F1 * cos(25) + F2 * cos(alpha)

Similarly, for the resultant force in the y direction, we can set up the following equation:

Ry = F1y + F2y + F3y

Since we want the resultant force to be directed along the positive u axis, we can set Ry equal to 0. This will give us the following equation:

0 = F1 * sin(25) + F2 * sin(alpha) + F3

Now, we have two equations and two unknowns (F2 and alpha). We can solve for F2 by rearranging the first equation to get:

F2 = (50 - F1 * cos(25)) / cos(alpha)

Then, we can substitute this value of F2 into the second equation and solve for alpha. Once we have the value of alpha, we can use it to solve for the angle theta by subtracting 25 degrees from alpha.

Overall, using the component method and setting up the equations in this way will
 

What is the purpose of finding theta of F2 in setting up forces?

The purpose of finding theta of F2 is to determine the direction of the second force (F2) in relation to the first force (F1). This is important in calculating the net force and understanding the overall motion of an object.

What information do I need to find theta of F2?

To find theta of F2, you will need to know the magnitude and direction of both forces (F1 and F2). This can be represented using vector notation or as components (x and y) of the forces.

How do I calculate theta of F2?

The formula for calculating theta of F2 is tan^-1(F2y/F2x), where F2y is the y-component of F2 and F2x is the x-component of F2. This will give you the angle in degrees or radians depending on the units used for the components.

Can theta of F2 be negative?

Yes, theta of F2 can be negative. This indicates that the direction of F2 is in the opposite direction of F1. However, when using vector notation, the angle will always be positive.

Why is it important to find the direction of F2 in setting up forces?

Finding the direction of F2 allows us to determine the overall motion of an object. If F2 is in the same direction as F1, the object will accelerate in that direction. If F2 is in the opposite direction, it will slow down the object. Knowing the direction of F2 is crucial in understanding the forces acting on an object.

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