Motion along a three-dimensional plane

In summary, the conversation discusses an example demonstrating Newton's laws in three dimensions, specifically focusing on incline motion. The equations for this motion are derived from Newton's second law and can be applied to a 3-dimensional system by finding a two-dimensional slice. The speaker is seeking assistance with deriving equations for a 3-dimensional system.
  • #1
leofil
1
0
Hi, I am working on an example that demonstrates Newtons laws in 3-dimensions (this is NOT homework). In my example I focus on incline (frictionless) motion, which can be represented as below in 2-dimensions.

http://imageshack.us/scaled/landing/855/212pxfreebodysvg.png


From Newtons second law (with proper choice of coordinate system) i get:
F_y:= 0 = N - mg cos(alpha)
F_x:= m a_x = f - mg sin(theta)
which then gives me N and a_x.

Can anybody help me with deriving a similar set of equations for a 3-dimensional system (xyz-system).
 
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  • #2
For three dimensions you can always find a two-dimensional slice.
 

Question 1: What is motion along a three-dimensional plane?

Motion along a three-dimensional plane refers to the movement of an object in three dimensions, often described using the x, y, and z axes. This type of motion is commonly seen in everyday life, such as objects moving through the air or vehicles traveling on roads.

Question 2: How is motion along a three-dimensional plane different from motion along a two-dimensional plane?

The main difference between motion along a three-dimensional plane and motion along a two-dimensional plane is the addition of the z axis. This allows for movement in three different directions instead of just two, making it a more complex type of motion to describe and analyze.

Question 3: What are some examples of motion along a three-dimensional plane?

Examples of motion along a three-dimensional plane include a ball being thrown through the air, a car driving on a winding road, a bird flying through the sky, and a rollercoaster moving along its track. Essentially, any type of movement that involves three dimensions can be considered motion along a three-dimensional plane.

Question 4: What is the role of vectors in motion along a three-dimensional plane?

In motion along a three-dimensional plane, vectors are used to represent both the direction and magnitude of an object's movement. The x, y, and z components of a vector can be used to describe the object's position, velocity, and acceleration at any given time.

Question 5: How is motion along a three-dimensional plane calculated and analyzed?

Motion along a three-dimensional plane is calculated and analyzed using mathematical equations and principles of physics, such as Newton's laws of motion and vector operations. By measuring an object's position, velocity, and acceleration in three dimensions, we can better understand and predict its movement.

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