Finding the components of this vector

In summary, a vector is a mathematical quantity with both magnitude and direction, often represented by an arrow. To find its components, you need to know its magnitude and direction and use trigonometric functions. The horizontal and vertical components are perpendicular and together form the vector. It is important to find these components as it allows for easier analysis and problem solving. Any vector can have its components found as long as its magnitude and direction are known, in both two and three dimensions.
  • #1
opticaltempest
135
0
How is the vector g turning into the scalar g? What am I missing that is
allowing us to represent g as a scalar quantity and no longer a vector
quantity? When going through the algebra to find mg_x, (component
of gravity in the x-direction) I don't see how it turns into a
scalar of 9.8.

http://img124.imageshack.us/img124/3417/page00023ue.jpg [Broken]
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
When they say [itex]g[/itex] instead of [itex]\vec{g}[/itex] they mean the magnitude of [itex]\vec{g}[/itex], i.e. [itex]g=|\vec{g}| = \sqrt{g_x^2 + g_y^2}[/itex].
 
  • #3


The vector g represents the acceleration due to gravity, which has both magnitude and direction. In order to find the components of this vector, we need to break it down into its x and y components. This is done using trigonometry and the angle of inclination shown in the diagram.

Once we have the x and y components of g, we can use them in equations to calculate the force of gravity in each direction. This is where the vector g turns into a scalar quantity.

A scalar quantity is a physical quantity that only has magnitude, without any direction. In this case, the force of gravity in the x-direction (mg_x) is a scalar quantity because it only represents the magnitude of the force, without any direction.

In order to find mg_x, we use the equation mg_x = mgcosθ, where θ is the angle of inclination. This equation only takes into account the magnitude of the force of gravity in the x-direction, without considering its direction. This is why it is represented as a scalar quantity.

You may be missing the fact that when we break down a vector into its components, we are essentially removing its direction and only considering its magnitude. This allows us to represent it as a scalar quantity, which simplifies the calculations and makes them easier to understand.

In summary, the vector g represents the acceleration due to gravity, but when we break it down into its components and use equations to calculate the force of gravity in each direction, it becomes a scalar quantity. This is because we are only considering its magnitude, without taking into account its direction.
 

What is a vector?

A vector is a mathematical quantity that has both magnitude and direction. It is often represented graphically as an arrow pointing in a specific direction with a specific length.

How do I find the components of a vector?

To find the components of a vector, you need to know its magnitude and direction. You can then use trigonometric functions to determine the horizontal and vertical components of the vector.

What are horizontal and vertical components of a vector?

The horizontal component of a vector is the part of the vector that lies along the x-axis, while the vertical component is the part that lies along the y-axis. These components are perpendicular to each other and together form the vector.

Why is it important to find the components of a vector?

Finding the components of a vector allows you to break down a complex vector into simpler parts, making it easier to analyze and manipulate. It also helps in solving mathematical problems involving vectors, such as calculating forces or velocities.

Can I find the components of any vector?

Yes, you can find the components of any vector as long as you know its magnitude and direction. This applies to both two-dimensional and three-dimensional vectors.

Similar threads

  • Introductory Physics Homework Help
2
Replies
44
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
631
  • Introductory Physics Homework Help
Replies
13
Views
522
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Advanced Physics Homework Help
Replies
0
Views
502
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top