Finding Resultant Force Using Cosine and Sine Law

In summary, the student attempted to solve the problem using the cosine and sine laws, but ended up with an incorrect answer because they subtracted the original force from the final result.
  • #1
Catchingupquickly
24
0

Homework Statement


"Calculate the net force with the resultant angle acting on each object indicated in the diagram."

The line going off to the southeast is supposed to be straight. My computer art skills aren't great.

| 22 N
|
|_ _ _ _ _
\ ) 35 degrees
\
\ 38 N​


2. Homework Equations

Cosine and sine law

The Attempt at a Solution



So the way the textbook teaches this is to redraw the diagram into a contained angle so that's what I did. I took the line that was 38 Newtons and shifted it so it still was in the exact same direction but now makes a contained angle with the 22 N force. I reckon that contained angle makes 55 degrees-- 180 - 35 - 90 = 55. I apologize for the word picture and not an actual picture. I don't know of a way to upload a picture of my work on paper on the forum.

From there I used cosine law (cosine and sine law is the method taught by my textbook to solve problems like this.)

## c^2 = a^2 + b^2 - 2ab Cos C
\\ = (38)^2 + (22)^2 - 2(38)(22) Cos C
\\ = \sqrt 968.98
\\ = 31.128##

Net force is 31 N

And sine law for the angle:

## {\frac {\sin A} a} = {\frac {\sin C} c}##

## {\frac {\sin A} {22}} = {\frac {\sin 55} {31}}##

Sin A = 0.581333708850252

The inverse = 35.54 or 36 degrees.

Now my textbook suggests that I need to subtract the original 35 degrees from this.

This makes the final answer Fnet = 31 N [ E 1 degree S]

Am I correct in any of this?
 
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  • #2
Catchingupquickly said:

Homework Statement


"Calculate the net force with the resultant angle acting on each object indicated in the diagram."

The line going off to the southeast is supposed to be straight. My computer art skills aren't great.

| 22 N
|
|_ _ _ _ _
\ ) 35 degrees
\
\ 38 N​


2. Homework Equations

Cosine and sine law

The Attempt at a Solution



So the way the textbook teaches this is to redraw the diagram into a contained angle so that's what I did. I took the line that was 38 Newtons and shifted it so it still was in the exact same direction but now makes a contained angle with the 22 N force. I reckon that contained angle makes 55 degrees-- 180 - 35 - 90 = 55. I apologize for the word picture and not an actual picture. I don't know of a way to upload a picture of my work on paper on the forum.

From there I used cosine law (cosine and sine law is the method taught by my textbook to solve problems like this.)

## c^2 = a^2 + b^2 - 2ab Cos C
\\ = (38)^2 + (22)^2 - 2(38)(22) Cos C
\\ = \sqrt 968.98
\\ = 31.128##

Net force is 31 N

And sine law for the angle:

## {\frac {\sin A} a} = {\frac {\sin C} c}##

## {\frac {\sin A} {22}} = {\frac {\sin 55} {31}}##

Sin A = 0.581333708850252

The inverse = 35.54 or 36 degrees.

Now my textbook suggests that I need to subtract the original 35 degrees from this.

This makes the final answer Fnet = 31 N [ E 1 degree S]

Am I correct in any of this?
You are correct in principle.
This is the figure showing the forces (blue and green) and the net force F (red).
Do not round off during the calculations. Rounding comes at the end when you give the result.
upload_2017-5-8_2-39-31.png


You can draw with any drawing program you have (I use Paint of Windows). Then you can copy and paste into your post.
 
  • #3
Thank you.
 

1. What is the difference between cosine and sine law?

Cosine law and sine law are both trigonometric formulas used to find the resultant force of a system. The main difference between the two is that cosine law is used to find the magnitude of the resultant force, while sine law is used to find the direction of the resultant force.

2. How do I use cosine law to find the magnitude of the resultant force?

To use cosine law, you will need to know the magnitudes and angles of the individual forces acting on the system. You can then use the formula F^2 = A^2 + B^2 - 2ABcosθ, where F is the magnitude of the resultant force, A and B are the magnitudes of the individual forces, and θ is the angle between the two forces.

3. When should I use sine law instead of cosine law?

Sine law should be used when you need to find the direction of the resultant force. This can be helpful in situations where you need to know the angle at which the forces are acting on the system.

4. Can cosine and sine law be used for any type of system?

Yes, cosine and sine law can be used for any type of system, as long as the forces acting on the system can be represented by vectors. These laws are particularly useful for solving problems in physics and engineering.

5. Are there any limitations to using cosine and sine law?

One limitation of using cosine and sine law is that they only work for systems where the forces are acting at a single point. If the forces are acting at multiple points, more advanced methods, such as vector addition, may be necessary to find the resultant force. Additionally, these laws only take into account two-dimensional systems and may not be applicable to three-dimensional systems.

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