Setting up systems of forces and free body diagrams

In summary, when setting up a free body diagram for a static mass on a downward plane, it is important to consider the weight and normal force as separate components. It is also important to note that the weight always points directly downwards, while the normal force is perpendicular to the incline. Therefore, it is correct to use the diagram shown in image B, as it accurately represents the direction of the weight and normal force.
  • #1
whitejac
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Homework Statement


Suppose I've got a static mass on a downward plane. (For instance a car on a drive way). How would you set up this free body diagram?

Homework Equations


F = f1+f2...etc

The Attempt at a Solution


image.jpeg

My preference is A, but I've seen it displayed in examples in my book as B. Is there and difference?
In the instance of this being a mass, I used A and said W could be broken down into components of W (for Wx and Wy) and that the normal force could be broken into X and Y as well for normal and frictional forces. The problem I see is that my X components will be opposite of how they are in real life. (I.e. The weight ought to be pointing toward the left because it will roll down the plane and friction ought to be pushing it up the plane). However, if you translate the system from a normal scenario to an inclined scenario (i.e. The left sketch to A) then it ought look like A.
 

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  • #2
No, image B is correct. The normal force is perpendicular to the incline, but the weight always points directly downwards (towards the center of the earth). As for your comment regarding the direction of the weight being in the direction of motion: if you project the weight vector onto the incline, you notice that some component of the weight is going to push the car to the left in image B. That isn't the case in image A.
 

Related to Setting up systems of forces and free body diagrams

What is a system of forces?

A system of forces is a collection of forces acting on a body or object. These forces can be internal or external, and they can be in equilibrium or unbalanced.

How do you draw a free body diagram?

To draw a free body diagram, you first identify the body or object that is being analyzed. Then, you draw a dot to represent the center of mass of the object. Next, you draw arrows to represent all the forces acting on the object, with the direction of the arrow indicating the direction of the force. Finally, you label each arrow with the name of the force and its magnitude.

Why is it important to set up systems of forces and free body diagrams?

Setting up systems of forces and free body diagrams allows us to analyze the forces acting on an object and understand how they affect its motion. This is crucial in fields such as engineering and physics, where understanding and predicting the behavior of objects is necessary.

What is the difference between internal and external forces?

Internal forces are forces that act within a body or object, such as tension or compression. External forces, on the other hand, act on the body from outside, such as gravity or contact forces. It is important to distinguish between these two types of forces when setting up systems and diagrams.

Can you have a system of forces in equilibrium with unbalanced forces?

No, a system of forces in equilibrium means that all the forces acting on the object are balanced, resulting in no net force and thus no acceleration. If there are unbalanced forces present, the system is not in equilibrium and the object will experience acceleration.

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