• masterflex
In summary, the conversation discusses a problem involving forces in space and the confusion caused by a missing minus sign in the solution. The individual posting the question seeks clarification on why the minus sign is necessary and how to determine its placement in the problem. Ultimately, it is revealed that the direction of the x-component of the tension CD is the key to understanding the role of the minus sign.
masterflex

## Homework Statement

see picture for problem.

## Homework Equations

please see a picture (one is of problem, the other contains the relevant formula).

## The Attempt at a Solution

I was able to solve the whole thing, then looked at the solution, and saw that I missed a minus sign (which changed some, but not all of my solutions). I just don't understand why that minus sign (denoted by red arrow) is necessary (besides giving you the right answer). Generally, how do you think through it to know you need one there? Thanks for you help.

#### Attachments

• 2.80.JPG
25.4 KB · Views: 433
• formulas.JPG
66.3 KB · Views: 428
Can you post your solution to the problem? The solution you posted is probably from the solutions manual which is meant for instructors, so they skip a lot of steps. It doesn't even show a FBD, so obviously it's difficult to understand their solution.

my work...

I've attached a picture of my work (where the minus sign confused me). And you can see that I get a different Theta_x.

My work:
theta_x = 75.5 degrees
theta_y = 30 degrees
theta_z = 64.3 degrees

solution book:
theta_x = 104.5 degrees
theta_y = 30 degrees
theta_z = 64.3 degrees

Also my force F (which is the force CD) has weird components that doesn't really reflect the correct direction. And I know it has to do with that minus sign that I'm struggling with (the minus sign that is pointed to by the red arrow in an earlier picture). I just can't make sense of that minus sign in a logical way.

Thank you.

#### Attachments

• 2.80_mywork.JPG
26 KB · Views: 413
Look at how the coordinate system is defined in the problem. Which direction is the x-component of the tension CD pointing?

that's it? awesome -- thanks a lot! It makes sense now.

## 1. Why is a minus sign used in forces in space problems?

The minus sign is used to indicate the direction of the force. In physics, forces can have both magnitude and direction. The minus sign represents a force in the opposite direction of the positive direction, which is usually designated as the right or forward direction.

## 2. How do we determine the direction of a force in space?

The direction of a force in space is determined by using a coordinate system. The x-axis is usually designated as the horizontal direction, the y-axis as the vertical direction, and the z-axis as the direction perpendicular to the x and y axes. The direction of the force is then described by the angles it makes with these axes, and the minus sign is used to indicate a force in the opposite direction of the positive axis.

## 3. Can we have negative forces in space?

Yes, we can have negative forces in space. As mentioned earlier, the minus sign represents the direction of the force, not the magnitude. A negative force simply means that the force is acting in the opposite direction of the positive direction. It does not indicate a weaker force compared to a positive force.

## 4. How does the minus sign affect the calculation of net force in space?

The minus sign does not affect the calculation of net force in space. In order to calculate the net force, we simply add all the forces acting on an object together, regardless of their direction. The minus sign is only used to indicate the direction of each individual force, but it does not impact the overall calculation.

## 5. Are there any special rules for using the minus sign in forces in space problems?

Yes, there are a few special rules to keep in mind when using the minus sign in forces in space problems. First, it is important to establish a consistent coordinate system and stick to it throughout the problem. Also, when adding forces, make sure to pay attention to the direction of each force and use the minus sign appropriately. Finally, be aware of any specific directions or angles mentioned in the problem and adjust the minus sign accordingly.

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