Deriving an equation through a free body diagram

In summary, the conversation discusses using a free body diagram to show that tan(\theta) = static friction on an incline plane. The suggested approach is to draw out the free body diagram and solve for the angle using the equation FF/FN = coefficient of friction. It is also mentioned that the question may need to be rephrased to show that tan(\theta) is less than or equal to the coefficient of static friction.
  • #1
xgdoyo
2
0

Homework Statement


Use a Free body diagram to show that :Tanθ=static friction, on an incline plane


Homework Equations



FF/FN= coeficiant of friction

The Attempt at a Solution


I know I must get an angle to have a tan of the Force of friction and a Normal force, but I don't understant why i need the the angle
 
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  • #2
You should draw out the free body diagram (since that's what the question asks) and that's usually the best way to go about solving these kinds of questions anyway.

What was the actual question? It would make more sense if it asked you to show that:
[tex]tan(\theta) \leq \mu_s [/tex]
(where [itex]\mu_s[/itex] is the coefficient of static friction). And remember that the friction force can be less than its maximum possible value, which is why there is an inequality sign.
 

1. What is a free body diagram and why is it important in deriving equations?

A free body diagram is a simplified representation of a physical system that shows all of the forces acting on an object. It is important in deriving equations because it allows us to clearly visualize and analyze the forces involved in a system, making it easier to apply Newton's laws of motion and ultimately derive equations that describe the behavior of the system.

2. How do I construct a free body diagram?

To construct a free body diagram, you must first identify the object of interest and all of the forces acting on it. Then, draw a simple sketch of the object, and label all of the forces with arrows indicating their direction and labels indicating their magnitude. Be sure to include the direction of motion and any fixed points or supports that may be involved.

3. What are some common forces that may appear on a free body diagram?

Some common forces that may appear on a free body diagram include weight, normal force, tension, friction, and applied forces. These forces may also have components in different directions, so it is important to consider all possible forces when constructing a free body diagram.

4. How do I use a free body diagram to derive an equation?

Once you have constructed a free body diagram, you can use it to apply Newton's laws of motion and determine the net force acting on the object. From there, you can use the principles of kinematics and other mathematical techniques to derive an equation that describes the motion of the object.

5. Can a free body diagram be used for any type of system?

Yes, a free body diagram can be used for any type of system, as long as the system can be represented by a simplified sketch with forces acting on it. It is a versatile tool that is commonly used in physics and engineering to analyze the behavior of various systems.

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